Introduction To Complex Numbers

By Anurag Singh
06-01-2019
2211

Introduction to complex numbers


Numbers can be divided into two types:

  1. Real numbers
  2. Complex numbers

Here we are going to study complex numbers (imaginary number)

A number which can be represented in the form a+ib where a,b are real numbers

For the complex number

Z= a+ib  where

a is called real part and is denoted by Re z

b is called imaginary part and is denoted by Im z

Of the complex number z.

For example,

Z= 3+4i

3 is called real part and 4 is called imaginary part.


Properties of complex numbers


  1. Addition of two complex numbers is a complex number.
  2. Difference of two complex number is a complex number
  3. Product of two complex numbers is a complex number.

For example,

Let z=a+ib and z'=c+id then zz' is

ZZ'= (ac-bd)+i(ad+bc)


Power of  complex number


Let √-1 be denoted by i then 

i=√-1

i²=-1

i³=i².i= -i

i⁴= i².i²= 1

And can be further solved in the same way .



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