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

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.

After going through Class 11 Complex number and Quadratic equation notes

Also, students can refer,

• NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers And Quadratic Equations
• NCERT Exemplar Class 11 Maths Chapter 5 Complex Numbers And Quadratic Equations

NCERT Class 11 Maths Chapter 5 Notes

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

Addition Of Two 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
Therefore xy=ac-bd+i(ad+bc)
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’

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,

Quadratic Equation

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.

Subject Wise NCERT Exemplar Solutions

• NCERT Exemplar Class 11 Solutions
• NCERT Exemplar Class 11 Maths
• NCERT Exemplar Class 11 Physics
• NCERT Exemplar Class 11 Chemistry
• NCERT Exemplar Class 11 Biology

Subject Wise NCERT Solutions

• NCERT Solutions for Class 11 Mathematics
• NCERT Solutions for Class 11 Chemistry
• NCERT Solutions for Class 11 Physics

• NCERT Solutions for Class 11 Biology

NCERT Books and Syllabus