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

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Modulus and Conjugate of a complex number

Modulus of complex number

 

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

mod of complex number

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

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 

conjugate of complex number1

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

conjugate of complex number 2
 Example Express the following in the form a + ib 

Solution

conjugate of complex number 3