Modulus and Conjugate of a complex number(Complex Number 2 NCERT)

Modulus and Conjugate of a complex number

Observe that the multiplicative inverse of the non-zero complex number z is given by 

Furthermore, the following results can easily be derived. 
For any two compex numbers z₁ and z₂, we have 
 

Example Find the multiplicative inverse of 2 – 3i. 
Solution Let z = 2 – 3i 
Then z̄ = 2 + 3i and |z|² = 2² + ( −3)² = 13 
Therefore, the multiplicative inverse of 2 − 3i is given by 

The above working can be reproduced in the following manner also,

 Example Express the following in the form a + ib 

Solution