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NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations are discussed here. These NCERT solutions are created by expert team at Careers360 keeping in mind of latest syllabus of CBSE 2023-24. in the earlier classes you have studied the quadratic equations. You must have come across some equations like x2 + 2 = 0, x2 = -2, for which there is no real solution. How to solve these quadratic equations? In this class 11 maths chapter 5 question answer, you will learn to solve equations like x2 + 2 = 0.
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The CBSE Syllabus for 2023 includes the chapter Complex Numbers and Quadratic Equations, which comprises significant mathematical theorems and formulae. The NCERT textbook provides ample practice problems to cover all these concepts, facilitating students' comprehension of advanced concepts in the future. To aid in this process, Careers360 offers detailed solutions for all complex numbers class 11 problems in the textbook. These complex numbers and quadratic equations class 11 solutions are particularly beneficial for students who aim to pass their exams with last-minute preparations. However, the primary focus of NCERT solutions for class 11 is to master concepts and develop a deeper understanding of the subject.
Complex Numbers:
A complex number is expressed as a + bi, where 'a' and 'b' are real numbers, and 'i' is the imaginary unit.
Imaginary Numbers: The square root of a negative real number is called an imaginary number, represented as √-1 = i.
Equality of Complex Number: Two complex numbers z1 = x1 + iy1 and z2 = x2 + iy2 are equal if x1 = x2 and y1 = y2.
Algebra of Complex Numbers:
Addition: (z1 + z2) = (x1 + x2) + i(y1 + y2)
Subtraction: (z1 - z2) = (x1 - x2) + i(y1 - y2)
Multiplication: (z1 * z2) = (x1x2 - y1y2) + i(x1y2 + x2y1)
Division: (z1 / z2) = [(x1x2 + y1y2) + i(x2y1 - x1y2)] / (x22 + y22), where z2 ≠ 0.
Conjugate of Complex Number: The conjugate of a complex number z = x + iy is represented as z¯ = x - iy.
Modulus of a Complex Number: |z| = √(x2 + y2)
Argument of a Complex Number: The angle made by the line joining the point z to the origin, with the positive X-axis in an anti-clockwise sense is called the argument (arg) of the complex number.
Principal Value of Argument:
When x > 0 and y > 0 ⇒ arg(z) = θ
When x < 0 and y > 0 ⇒ arg(z) = π - θ
When x < 0 and y < 0 ⇒ arg(z) = -(π - θ)
When x > 0 and y < 0 ⇒ arg(z) = -θ
Polar Form of a Complex Number: z = |z| (cosθ + isinθ), where θ = arg(z).
The general polar form of z is z = |z| [cos(2nπ + θ) + isin(2nπ + θ)], where n is an integer.
Free download NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations for CBSE Exam.
Class 11 maths chapter 5 NCERT solutions - Exercise: 5.1
Question:1 Express each of the complex number in the form .
Answer:
On solving
we will get
Now, in the form of we can write it as
Question:2 Express each of the complex number in the form .
Answer:
We know that
Now, we will reduce into
Now, in the form of we can write it as
Therefore, the answer is
Question:3 Express each of the complex number in the form a+ib.
Answer:
We know that
Now, we will reduce into
Now, in the form of we can write it as
Therefore, the answer is
Question:4 Express each of the complex number in the form a+ib.
Answer:
Given problem is
Now, we will reduce it into
Therefore, the answer is
Question:5 Express each of the complex number in the form .
Answer:
Given problem is
Now, we will reduce it into
Therefore, the answer is
Question:6 Express each of the complex number in the form .
Answer:
Given problem is
Now, we will reduce it into
Therefore, the answer is
Question:7 Express each of the complex number in the form .
Answer:
Given problem is
Now, we will reduce it into
Therefore, the answer is
Question:8 Express each of the complex number in the form .
Answer:
The given problem is
Now, we will reduce it into
Therefore, the answer is
Question:9 Express each of the complex number in the form .
Answer:
Given problem is
Now, we will reduce it into
Therefore, the answer is
Question:10 Express each of the complex number in the form .
Answer:
Given problem is
Now, we will reduce it into
Therefore, the answer is
Question:11 Find the multiplicative inverse of each of the complex numbers.
Answer:
Let
Then,
And
Now, the multiplicative inverse is given by
Therefore, the multiplicative inverse is
Question:12 Find the multiplicative inverse of each of the complex numbers.
Answer:
Let
Then,
And
Now, the multiplicative inverse is given by
Therefore, the multiplicative inverse is
Question:13 Find the multiplicative inverse of each of the complex numbers.
Answer:
Let
Then,
And
Now, the multiplicative inverse is given by
Therefore, the multiplicative inverse is
Question:14 Express the following expression in the form of
Answer:
Given problem is
Now, we will reduce it into
Therefore, answer is
Class 11 maths chapter 5 ncert solutions - Exercise: 5.2
Question:1 Find the modulus and the arguments of each of the complex numbers.
Answer:
Given the problem is
Now, let
Square and add both the sides
Therefore, the modulus is 2
Now,
Since, both the values of is negative and we know that they are negative in III quadrant
Therefore,
Argument =
Therefore, the argument is
Question:2 Find the modulus and the arguments of each of the complex numbers.
Answer:
Given the problem is
Now, let
Square and add both the sides
Therefore, the modulus is 2
Now,
Since values of is negative and value is positive and we know that this is the case in II quadrant
Therefore,
Argument =
Therefore, the argument is
Question:3 Convert each of the complex numbers in the polar form:
Answer:
Given problem is
Now, let
Square and add both the sides
Therefore, the modulus is
Now,
Since values of is negative and value is positive and we know that this is the case in the IV quadrant
Therefore,
Therefore,
Therefore, the required polar form is
Question:4 Convert each of the complex numbers in the polar form:
Answer:
Given the problem is
Now, let
Square and add both the sides
Therefore, the modulus is
Now,
Since values of is negative and value is positive and we know that this is the case in II quadrant
Therefore,
Therefore,
Therefore, the required polar form is
Question:5 Convert each of the complex numbers in the polar form:
Answer:
Given problem is
Now, let
Square and add both the sides
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Therefore, the modulus is
Now,
Since values of both and is negative and we know that this is the case in III quadrant
Therefore,
Therefore,
Therefore, the required polar form is
Question:6 Convert each of the complex numbers in the polar form:
Answer:
Given problem is
Now, let
Square and add both the sides
Therefore, the modulus is 3
Now,
Since values of is negative and is Positive and we know that this is the case in II quadrant
Therefore,
Therefore,
Therefore, the required polar form is
Question:7 Convert each of the complex numbers in the polar form:
Answer:
Given problem is
Now, let
Square and add both the sides
Therefore, the modulus is 2
Now,
Since values of Both and is Positive and we know that this is the case in I quadrant
Therefore,
Therefore,
Therefore, the required polar form is
Question:8 Convert each of the complex numbers in the polar form:
Answer:
Given problem is
Now, let
Square and add both the sides
Therefore, the modulus is 1
Now,
Since values of Both and is Positive and we know that this is the case in I quadrant
Therefore,
Therefore,
Therefore, the required polar form is
Class 11 maths chapter 5 ncert solutions - Exercise: 5.3
Question:1 Solve each of the following equations:
Answer:
Given equation is
Now, we know that the roots of the quadratic equation is given by the formula
In this case value of a = 1 , b = 0 and c = 3
Therefore,
Therefore, the solutions of requires equation are
Question:2 Solve each of the following equations:
Answer:
Given equation is
Now, we know that the roots of the quadratic equation are given by the formula
In this case value of a = 2 , b = 1 and c = 1
Therefore,
Therefore, the solutions of requires equation are
Question:3 Solve each of the following equations:
Answer:
Given equation is
Now, we know that the roots of the quadratic equation are given by the formula
In this case value of a = 1 , b = 3 and c = 9
Therefore,
Therefore, the solutions of requires equation are
Question:4 Solve each of the following equations:
Answer:
Given equation is
Now, we know that the roots of the quadratic equation is given by the formula
In this case value of a = -1 , b = 1 and c = -2
Therefore,
Therefore, the solutions of equation are
Question:5 Solve each of the following equations:
Answer:
Given equation is
Now, we know that the roots of the quadratic equation are given by the formula
In this case value of a = 1 , b = 3 and c = 5
Therefore,
Therefore, the solutions of the equation are
Question:6 Solve each of the following equations:
Answer:
Given equation is
Now, we know that the roots of the quadratic equation are given by the formula
In this case value of a = 1 , b = -1 and c = 2
Therefore,
Therefore, the solutions of equation are
Question:7 Solve each of the following equations:
Answer:
Given equation is
Now, we know that the roots of the quadratic equation is given by the formula
In this case the value of
Therefore,
Therefore, the solutions of the equation are
Question:8 Solve each of the following equations:
Answer:
Given equation is
Now, we know that the roots of the quadratic equation are given by the formula
In this case the value of
Therefore,
Therefore, the solutions of the equation are
Question:9 Solve each of the following equations:
Answer:
Given equation is
Now, we know that the roots of the quadratic equation is given by the formula
In this case the value of
Therefore,
Therefore, the solutions of the equation are
Question:10 Solve each of the following equations:
Answer:
Given equation is
Now, we know that the roots of the quadratic equation are given by the formula
In this case the value of
Therefore,
Therefore, the solutions of the equation are
Complex numbers and quadratic equations class 11 solutions - Miscellaneous Exercise
Question:1 Evaluate .
Answer:
The given problem is
Now, we will reduce it into
Now,
Therefore, answer is
Question:2 For any two complex numbers and , prove that
Answer:
Let two complex numbers are
Now,
Hence proved
Question:3 Reduce to the standard form.
Answer:
Given problem is
Now, we will reduce it into
Now, multiply numerator an denominator by
Therefore, answer is
Question:4 If , prove that
Answer:
the given problem is
Now, multiply the numerator and denominator by
Now, square both the sides
On comparing the real and imaginary part, we obtain
Now,
Hence proved
Question:5(i) Convert the following in the polar form:
Answer:
Let
Now, multiply the numerator and denominator by
Now,
let
On squaring both and then add
Now,
Since the value of is negative and is positive this is the case in II quadrant
Therefore,
Therefore, the required polar form is
Question:5(ii) Convert the following in the polar form:
Answer:
Let
Now, multiply the numerator and denominator by
Now,
let
On squaring both and then add
Now,
Since the value of is negative and is positive this is the case in II quadrant
Therefore,
Therefore, the required polar form is
Question:6 Solve each of the equation:
Answer:
Given equation is
Now, we know that the roots of the quadratic equation are given by the formula
In this case the value of
Therefore,
Therefore, the solutions of requires equation are
Question:7 Solve each of the equation:
Answer:
Given equation is
Now, we know that the roots of the quadratic equation are given by the formula
In this case the value of
Therefore,
Therefore, the solutions of requires equation are
Question:8 Solve each of the equation: .
Answer:
Given equation is
Now, we know that the roots of the quadratic equation are given by the formula
In this case the value of
Therefore,
Therefore, the solutions of requires equation are
Question:9 Solve each of the equation:
Answer:
Given equation is
Now, we know that the roots of the quadratic equation are given by the formula
In this case the value of
Therefore,
Therefore, the solutions of requires equation are
Question:10 If , find .
Answer:
It is given that
Then,
Now, multiply the numerator and denominator by
Now,
Therefore, the value of
is
Question:11 If , prove that .
Answer:
It is given that
Now, we will reduce it into
On comparing real and imaginary part. we will get
Now,
Hence proved
Question:12(ii) Let Find
Answer:
It is given that
Therefore,
NOw,
Now,
Therefore,
Therefore, the answer is 0
Question:13 Find the modulus and argument of the complex number .
Answer:
Let
Now, multiply the numerator and denominator by
Therefore,
Square and add both the sides
Therefore, the modulus is
Now,
Since the value of is negative and the value of is positive and we know that it is the case in II quadrant
Therefore,
Argument
Therefore, Argument and modulus are respectively
Question:14 Find the real numbers x andy if is the conjugate of .
Answer:
Let
Therefore,
Now, it is given that
Compare (i) and (ii) we will get
On comparing real and imaginary part. we will get
On solving these we will get
Therefore, the value of x and y are 3 and -3 respectively
Question:15 Find the modulus of .
Answer:
Let
Now, we will reduce it into
Now,
square and add both the sides. we will get,
Therefore, modulus of
is 2
Question:16 If , then show that
Answer:
it is given that
Now, expand the Left-hand side
On comparing real and imaginary part. we will get,
Now,
Hence proved
Question:17 If and are different complex numbers with , then find .
Answer:
Let
and
It is given that
and
Now,
Therefore, value of is 1
Question:18 Find the number of non-zero integral solutions of the equation .
Answer:
Given problem is
Now,
x = 0 is the only possible solution to the given problem
Therefore, there are 0 number of non-zero integral solutions of the equation
Question:19 If then show that
Answer:
It is given that
Now, take mod on both sides
Square both the sides. we will get
Hence proved
Question:20 If then find the least positive integral value of .
Answer:
Let
Now, multiply both numerator and denominator by
We will get,
We know that
Therefore, the least positive integral value of is 4
The NCERT Solutions for Chapter 5 - Complex Numbers and Quadratic Equations in Class 11 Maths consists of 3 exercises and a miscellaneous exercise to provide enough practice problems for the students to comprehend all the concepts. The PDF of NCERT Solutions for Class 11 Maths includes detailed explanations of the following topics and sub-topics:
This section of ch 5 maths class 11 covers quadratic equations with no real solutions and their solutions using complex numbers. The solution to the quadratic equation ax^2 + bx + c = 0 has been derived when the discriminant D = b^2 - 4ac is less than 0.
5.3.1 Addition of two complex numbers
5.3.2 Difference of two complex numbers
5.3.3 Multiplication of two complex numbers
5.3.4 Division of two complex number
5.3.5 Power of i
5.3.6 The square roots of a negative real number
5.3.7 Identities
After completing these exercises of complex no class 11 , students will have a better understanding of the fundamental BODMAS operations on complex numbers, as well as their properties, the power of i, square roots of negative real numbers, and complex number identitie
chapter-1 | Sets |
chapter-2 | Relations and Functions |
chapter-3 | Trigonometric Functions |
chapter-4 | Principle of Mathematical Induction |
chapter-5 | Complex Numbers and Quadratic equations |
chapter-6 | Linear Inequalities |
chapter-7 | Permutation and Combinations |
chapter-8 | Binomial Theorem |
chapter-9 | Sequences and Series |
chapter-10 | Straight Lines |
chapter-11 | Conic Section |
chapter-12 | Introduction to Three Dimensional Geometry |
chapter-13 | Limits and Derivatives |
chapter-14 | Mathematical Reasoning |
chapter-15 | Statistics |
chapter-16 | Probability |
Clarity of concepts: The NCERT Solutions for maths chapter 5 class 11 provide clear explanations and examples that help students to understand the concepts easily. The solutions are designed to make the learning process easier and more enjoyable.
Practice: The class 11 complex numbers and quadratic equations NCERT solutions come with a wide range of practice problems that help students to practice and master the concepts covered in the chapter. The more problems they solve, the better they become at the topic.
Exam preparation: NCERT Solutions for ch 5 maths class 11 are designed to help students prepare for their exams. The solutions provide a comprehensive overview of the chapter, including all the important topics and subtopics.
NCERT solutions for class 11 biology |
NCERT solutions for class 11 maths |
NCERT solutions for class 11 chemistry |
NCERT solutions for class 11 physics |
Complex Numbers And Quadratic Equation Class 11 Chapter-Some Important Point To Remember
As mentioned in the first paragraph and
and any number can be represented as a complex number of the form a+ ib where a is the real part and b is the imaginary part, for example, 1=1+0i.
So a complex number of the form a+ ib can be represented as
and
and the above representation is known as the polar form of a complex number. T he polar form of the complex number makes the problem very easy to solve. There are many problems in the NCERT solutions for class 11 maths chapter 5 complex numbers and quadratic equations which are explained using the polar form of the complex number and some are solved using 2-D geometry. So, NCERT solutions for class 11 maths chapter 5 complex numbers and quadratic equations can make learning easier for you so that you can score well.
Happy Reading !!!
Class 11 maths NCERT solutions chapter 5 includes topics such as Complex numbers, algebra of complex numbers, modulus and the conjugate of a complex number, argand plane and polar representation, and quadratic equations are the important topics in this chapter. to get command in these topics students can practice problems from complex numbers class 11 pdf.
NCERT solutions are highly beneficial for students as they provide well-structured and comprehensive solutions to the textbook questions. These solutions are designed by subject matter experts and cover all the important topics and concepts in a clear and concise manner. Students can practice complex numbers class 11 solutions to get good hold on the concepts of chapter 5 class 11.
Most of the students consider permutation and combination, trigonometry as the most difficult chapters in class 11 maths but with the rigorous practice students can get command on them also.
There are 16 chapters starting from set to probability in the CBSE class 11 maths.
No, CBSE doesn’t provided NCERT solutions for any class or subject.
Here you will get the detailed NCERT solutions for class 11 maths by clicking on the link.
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For an individual who opts for a career as an actor, the primary responsibility is to completely speak to the character he or she is playing and to persuade the crowd that the character is genuine by connecting with them and bringing them into the story. This applies to significant roles and littler parts, as all roles join to make an effective creation. Here in this article, we will discuss how to become an actor in India, actor exams, actor salary in India, and actor jobs.
Individuals who opt for a career as acrobats create and direct original routines for themselves, in addition to developing interpretations of existing routines. The work of circus acrobats can be seen in a variety of performance settings, including circus, reality shows, sports events like the Olympics, movies and commercials. Individuals who opt for a career as acrobats must be prepared to face rejections and intermittent periods of work. The creativity of acrobats may extend to other aspects of the performance. For example, acrobats in the circus may work with gym trainers, celebrities or collaborate with other professionals to enhance such performance elements as costume and or maybe at the teaching end of the career.
Career as a video game designer is filled with excitement as well as responsibilities. A video game designer is someone who is involved in the process of creating a game from day one. He or she is responsible for fulfilling duties like designing the character of the game, the several levels involved, plot, art and similar other elements. Individuals who opt for a career as a video game designer may also write the codes for the game using different programming languages.
Depending on the video game designer job description and experience they may also have to lead a team and do the early testing of the game in order to suggest changes and find loopholes.
Radio Jockey is an exciting, promising career and a great challenge for music lovers. If you are really interested in a career as radio jockey, then it is very important for an RJ to have an automatic, fun, and friendly personality. If you want to get a job done in this field, a strong command of the language and a good voice are always good things. Apart from this, in order to be a good radio jockey, you will also listen to good radio jockeys so that you can understand their style and later make your own by practicing.
A career as radio jockey has a lot to offer to deserving candidates. If you want to know more about a career as radio jockey, and how to become a radio jockey then continue reading the article.
The word “choreography" actually comes from Greek words that mean “dance writing." Individuals who opt for a career as a choreographer create and direct original dances, in addition to developing interpretations of existing dances. A Choreographer dances and utilises his or her creativity in other aspects of dance performance. For example, he or she may work with the music director to select music or collaborate with other famous choreographers to enhance such performance elements as lighting, costume and set design.
A career as social media manager involves implementing the company’s or brand’s marketing plan across all social media channels. Social media managers help in building or improving a brand’s or a company’s website traffic, build brand awareness, create and implement marketing and brand strategy. Social media managers are key to important social communication as well.
Photography is considered both a science and an art, an artistic means of expression in which the camera replaces the pen. In a career as a photographer, an individual is hired to capture the moments of public and private events, such as press conferences or weddings, or may also work inside a studio, where people go to get their picture clicked. Photography is divided into many streams each generating numerous career opportunities in photography. With the boom in advertising, media, and the fashion industry, photography has emerged as a lucrative and thrilling career option for many Indian youths.
An individual who is pursuing a career as a producer is responsible for managing the business aspects of production. They are involved in each aspect of production from its inception to deception. Famous movie producers review the script, recommend changes and visualise the story.
They are responsible for overseeing the finance involved in the project and distributing the film for broadcasting on various platforms. A career as a producer is quite fulfilling as well as exhaustive in terms of playing different roles in order for a production to be successful. Famous movie producers are responsible for hiring creative and technical personnel on contract basis.
In a career as a copywriter, one has to consult with the client and understand the brief well. A career as a copywriter has a lot to offer to deserving candidates. Several new mediums of advertising are opening therefore making it a lucrative career choice. Students can pursue various copywriter courses such as Journalism, Advertising, Marketing Management. Here, we have discussed how to become a freelance copywriter, copywriter career path, how to become a copywriter in India, and copywriting career outlook.
In a career as a vlogger, one generally works for himself or herself. However, once an individual has gained viewership there are several brands and companies that approach them for paid collaboration. It is one of those fields where an individual can earn well while following his or her passion.
Ever since internet costs got reduced the viewership for these types of content has increased on a large scale. Therefore, a career as a vlogger has a lot to offer. If you want to know more about the Vlogger eligibility, roles and responsibilities then continue reading the article.
For publishing books, newspapers, magazines and digital material, editorial and commercial strategies are set by publishers. Individuals in publishing career paths make choices about the markets their businesses will reach and the type of content that their audience will be served. Individuals in book publisher careers collaborate with editorial staff, designers, authors, and freelance contributors who develop and manage the creation of content.
Careers in journalism are filled with excitement as well as responsibilities. One cannot afford to miss out on the details. As it is the small details that provide insights into a story. Depending on those insights a journalist goes about writing a news article. A journalism career can be stressful at times but if you are someone who is passionate about it then it is the right choice for you. If you want to know more about the media field and journalist career then continue reading this article.
Individuals in the editor career path is an unsung hero of the news industry who polishes the language of the news stories provided by stringers, reporters, copywriters and content writers and also news agencies. Individuals who opt for a career as an editor make it more persuasive, concise and clear for readers. In this article, we will discuss the details of the editor's career path such as how to become an editor in India, editor salary in India and editor skills and qualities.
Individuals who opt for a career as a reporter may often be at work on national holidays and festivities. He or she pitches various story ideas and covers news stories in risky situations. Students can pursue a BMC (Bachelor of Mass Communication), B.M.M. (Bachelor of Mass Media), or MAJMC (MA in Journalism and Mass Communication) to become a reporter. While we sit at home reporters travel to locations to collect information that carries a news value.
Are you searching for a Corporate Executive job description? A Corporate Executive role comes with administrative duties. He or she provides support to the leadership of the organisation. A Corporate Executive fulfils the business purpose and ensures its financial stability. In this article, we are going to discuss how to become corporate executive.
A multimedia specialist is a media professional who creates, audio, videos, graphic image files, computer animations for multimedia applications. He or she is responsible for planning, producing, and maintaining websites and applications.
Welding Engineer Job Description: A Welding Engineer work involves managing welding projects and supervising welding teams. He or she is responsible for reviewing welding procedures, processes and documentation. A career as Welding Engineer involves conducting failure analyses and causes on welding issues.
A quality controller plays a crucial role in an organisation. He or she is responsible for performing quality checks on manufactured products. He or she identifies the defects in a product and rejects the product.
A quality controller records detailed information about products with defects and sends it to the supervisor or plant manager to take necessary actions to improve the production process.
A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.
A QA Lead is in charge of the QA Team. The role of QA Lead comes with the responsibility of assessing services and products in order to determine that he or she meets the quality standards. He or she develops, implements and manages test plans.
A Structural Engineer designs buildings, bridges, and other related structures. He or she analyzes the structures and makes sure the structures are strong enough to be used by the people. A career as a Structural Engineer requires working in the construction process. It comes under the civil engineering discipline. A Structure Engineer creates structural models with the help of computer-aided design software.
The Process Development Engineers design, implement, manufacture, mine, and other production systems using technical knowledge and expertise in the industry. They use computer modeling software to test technologies and machinery. An individual who is opting career as Process Development Engineer is responsible for developing cost-effective and efficient processes. They also monitor the production process and ensure it functions smoothly and efficiently.
An AWS Solution Architect is someone who specializes in developing and implementing cloud computing systems. He or she has a good understanding of the various aspects of cloud computing and can confidently deploy and manage their systems. He or she troubleshoots the issues and evaluates the risk from the third party.
An Azure Administrator is a professional responsible for implementing, monitoring, and maintaining Azure Solutions. He or she manages cloud infrastructure service instances and various cloud servers as well as sets up public and private cloud systems.
Careers in computer programming primarily refer to the systematic act of writing code and moreover include wider computer science areas. The word 'programmer' or 'coder' has entered into practice with the growing number of newly self-taught tech enthusiasts. Computer programming careers involve the use of designs created by software developers and engineers and transforming them into commands that can be implemented by computers. These commands result in regular usage of social media sites, word-processing applications and browsers.
A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.
Individuals in the information security manager career path involves in overseeing and controlling all aspects of computer security. The IT security manager job description includes planning and carrying out security measures to protect the business data and information from corruption, theft, unauthorised access, and deliberate attack
An Automation Test Engineer job involves executing automated test scripts. He or she identifies the project’s problems and troubleshoots them. The role involves documenting the defect using management tools. He or she works with the application team in order to resolve any issues arising during the testing process.
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