Complex Numbers And Quadratic Equations Class 11th Notes - Free NCERT Class 11 Maths Chapter 5 notes - Download PDF

Complex Numbers And Quadratic Equations Class 11th Notes - Free NCERT Class 11 Maths Chapter 5 notes - Download PDF

Edited By Ramraj Saini | Updated on Mar 22, 2022 04:46 PM IST

Complex number and Quadratic equation belong to the 5 chapter of NCERT. The NCERT Class 11 Maths chapter 5 notes cover up the important topics of the chapter Complex number and Quadratic equation. Class 11 Math chapter 5 notes also contain important formulas of the chapter.

Class 11 Maths chapter 5 note contains systematic explanations of topics using examples and exercises. Notes for Class 11 Maths chapter 5 includes topics starting from algebra of Complex number to Quadratic equation. NCERT Notes for Class 11 Maths chapter 5 not only covers the NCERT notes but covers CBSE Class 11 Maths chapter 5 notes also.

JEE Main Scholarship Test Kit (Class 11): Narayana | Physics WallahAakash Unacademy

Scholarship Test: Vidyamandir Intellect Quest (VIQ)

After going through Class 11 Complex number and Quadratic equation notes

Also, students can refer,

Complex Number

A complex number is defined as the combination of real and imaginary numbers.

Example: 3+4i

Here 3 is real and 4i is the imaginary part.

Here is i =√(-1), then we can say that i²=-1

Algebra Of Complex Number

Let x=a+ib and y=c+id

Therefore x+y= (a+c) +i(b+d)

Properties

• The closure law The sum of two complex numbers is also a complex number

• The commutative law x+y=y+x

• The associative law (x+y)+z=x+(y+z)

Difference Of Two Complex Number
Let x=a+ib and y=c+id
Therefore x-y= x+(-y)
Multiplication On Two Complex Number
Let x=a+ib and y=c+id
Properties

• The closure law The multiplication of two complex numbers is also a complex number

• The commutative law xy=yx

• The associative law (xy)z=x(yz)

• The distributive law x(y+z) = xy+xz and (x+y)z=xz+yz

Division Of Two Complex Number

Let x=a+ib and y=c+id

Therefore x/y=x.(1/y)

Power Of i

In general, any integer k

The square roots of a negative real number

The Modulus And The Conjugate Of A Complex Number

Properties

1. |x y|=|x||y|

2. |x/y|=|x|/|y|

3. (xy)'=x'y'

4. (x±y)’=x’±y’

5. (x/y)’=x’/y’

JEE Main Highest Scoring Chapters & Topics
Just Study 40% Syllabus and Score upto 100%

Argand Plane And Polar Representation

The complex number a+ib corresponding to ordered pairs (a, b) can also be represented geometrically in the XY plane.

In the argand plane, the modulus of complex number a+ib =√(a²+b²) is the distance from the origin to the point.

Polar Representation Of A Complex Number

We note that the point P is uniquely determined by the ordered pair of real numbers (r, θ), called the polar coordinates of the point P.

We get a=rcosθ, b=rsinθ, thus x=r(cosθ +i sin θ)

Example:

Express the following in the form a + ib,

The equation that consists of the highest power in the polynomial is 2.

Let ax²+bx+c=0 be a quadric equation then its discriminant is

D=b²-4ac

Let us assume that D<0

Example:

Solve x²+x+1=0

Solution:

Here, b²-4ac=12-4*1*1=-3

This becomes the end of the chapter

Significance of NCERT Class 11 Math Chapter 5 Notes

Class 11 complex number and quadratic equation notes will help to understand the formulas, statements, rules in detail. Also Class 11 Math Chapter 5 Notes is helpful to study the important topics covered by class 11 CBSE Syllabuses Class 11 Maths chapter 5 notes pdf download can be used for preparing offline and solving problems.

NCERT Class 11 Notes Chapter Wise.

 NCERT Class 11 Maths Chapter 1 Notes NCERT Class 11 Maths Chapter 2 Notes NCERT Class 11 Maths Chapter 3 Notes NCERT Class 11 Maths Chapter 4 Notes NCERT Class 11 Maths Chapter 5 Notes NCERT Class 11 Maths Chapter 6 Notes NCERT Class 11 Maths Chapter 7 Notes NCERT Class 11 Maths Chapter 8 Notes NCERT Class 11 Maths Chapter 9 Notes NCERT Class 11 Maths Chapter 10 Notes NCERT Class 11 Maths Chapter 11 Notes NCERT Class 11 Maths Chapter 12 Notes NCERT Class 11 Maths Chapter 13 Notes NCERT Class 11 Maths Chapter 14 Notes NCERT Class 11 Maths Chapter 15 Notes NCERT Class 11 Maths Chapter 16 Notes

NCERT Books and Syllabus

 NCERT Book for Class 11 NCERT Syllabus for Class 11

1. Define quadratic equation according to Class 11 Maths chapter 5 notes.

The equation that consists of the highest power in the polynomial is 2.

2. Define Complex number as per NCERT notes for Class 11 Maths chapter 5.

A complex number is defined as the combination of real and imaginary numbers.

3. Is zero a complex number?

According to Class 12 Math chapter 7 textbook, zero is a complex number.

4. What are imaginary numbers according to NCERT Class 11 Maths chapter 5 notes?

The numbers are called imaginary if it gives negative value when squared.

Upcoming School Exams

National Means Cum-Merit Scholarship

Application Date:01 August,2024 - 16 September,2024

National Rural Talent Scholarship Examination

Application Date:05 September,2024 - 20 September,2024

Nagaland Board High School Leaving Certificate Examination

Application Date:17 September,2024 - 30 September,2024

Nagaland Board of Secondary Education 12th Examination

Application Date:17 September,2024 - 30 September,2024

Exam Date:19 September,2024 - 19 September,2024

Get answers from students and experts

A block of mass 0.50 kg is moving with a speed of 2.00 ms-1 on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is

 Option 1) Option 2) Option 3) Option 4)

A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times.  Assume that the potential energy lost each time he lowers the mass is dissipated.  How much fat will he use up considering the work done only when the weight is lifted up ?  Fat supplies 3.8×107 J of energy per kg which is converted to mechanical energy with a 20% efficiency rate.  Take g = 9.8 ms−2 :

 Option 1) 2.45×10−3 kg Option 2)  6.45×10−3 kg Option 3)  9.89×10−3 kg Option 4) 12.89×10−3 kg

An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

 Option 1) Option 2) Option 3) Option 4)

A particle is projected at 600   to the horizontal with a kinetic energy . The kinetic energy at the highest point

 Option 1) Option 2) Option 3) Option 4)

In the reaction,

 Option 1)   at STP  is produced for every mole   consumed Option 2)   is consumed for ever      produced Option 3) is produced regardless of temperature and pressure for every mole Al that reacts Option 4) at STP is produced for every mole Al that reacts .

How many moles of magnesium phosphate, will contain 0.25 mole of oxygen atoms?

 Option 1) 0.02 Option 2) 3.125 × 10-2 Option 3) 1.25 × 10-2 Option 4) 2.5 × 10-2

If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will

 Option 1) decrease twice Option 2) increase two fold Option 3) remain unchanged Option 4) be a function of the molecular mass of the substance.

With increase of temperature, which of these changes?

 Option 1) Molality Option 2) Weight fraction of solute Option 3) Fraction of solute present in water Option 4) Mole fraction.

Number of atoms in 558.5 gram Fe (at. wt.of Fe = 55.85 g mol-1) is

 Option 1) twice that in 60 g carbon Option 2) 6.023 × 1022 Option 3) half that in 8 g He Option 4) 558.5 × 6.023 × 1023

A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t2) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m2 , the number of rotations made by the pulley before its direction of motion if reversed, is

 Option 1) less than 3 Option 2) more than 3 but less than 6 Option 3) more than 6 but less than 9 Option 4) more than 9