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