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

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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

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