- What is complex numbers
- |
- Properties Of complex Numbers
- |
- Conjugate of Complex Numbers
- |
- Modulus of complex numbers
- |
- Graphical Representation of Complex Number
- |
- Polar Representation of the complex number
- |
- Rotation of Complex Number
- |
- What is the significance of Complex Numbers

Complex numbers are the numbers of the form a+ib where $ i=\sqrt{(-1)}$ and a and b are real numbers.

**Definition:-** Complex numbers are defined as an ordered pair of real numbers like (x,y) where

$z=(x,y)=x+iy$

and both x and y are real numbers and x is known as real part of complex number and y is known as imaginary part of the complex number.

**Example**

z_{1}= 2+4i

z_{1}= 8-4i

**Addition of complex numbers**

Let z_{1}=x_{1}+iy_{1} and z_{2}=x_{2}+iy_{2} then

z_{1}+z_{2}=(x_{1}+x_{2})+i(y_{1}+y_{2})

**Subtraction**

z_{1}-z_{2}=(x_{1}-x_{2})+i(y_{1}-y_{2})

**Multiplication**

(z_{1}.z_{2})=(x_{1}+iy_{1}).(x_{2}+iy_{2})

**Multiplicative Inverse**

for z=x+iy

z^{-1} is given by

=$(\frac{a}{a^{2}+b^{2}})+i(\frac{-b}{a^{2}+b^{2}})$

**Division**

To divide complex number by another , first write quotient as a fraction. Then reduce the denominator complex number to multiplicative Inverse and then simple multiplication applies

**Example**

Find the value of

(1+i)/(1+2i)

**Solution:**

The multiplicative inverse of (1+2i) is given

as

=$(\frac{a}{a^{2}+b^{2}})+i(\frac{-b}{a^{2}+b^{2}})$

=(1/5-2i/5)

So (1+i)/(1+2i)

=(1+i)(1/5-2i/5)

=1/5-2i/5+ i/5+2/5

=-i/5 +3/5

Go Back to Class 11 Maths Home page Go Back to Class 11 Physics Home page

- Mathematics - Class 11 by RD Sharma
- NCERT Exemplar Problems: Solutions Mathematics Class 11
- NCERT Solutions: Mathematics Class 11th
- Mathematics Textbook for Class XI
- Cbse Mathematics for Class XI (Thoroughly Revised As Per New Cbse Syllabus)
- 37 Years Chapterwise Solved Papers (2015-1979): IIT JEE - Mathematics
- Play with Graphs - Skills in Mathematics for JEE Main and Advanced