Question

What is the multiplicative inverse of 6 + 2i?

Answer 1

We have to multiply (6 + 2i) with its conjugate:
(6 + 2i) (6 - 2i) = 36-12i+12i-4i^2
As i^2= -1 . So ,
= 36+4
= 40
So 40 +is the correct answer.

Answer 2

The product of a number and it multiplicative inverse is 1. Let the multiplicative inverse of 6 + 2i be x. Then
x(6 + 2i) = 1
x = 1/(6 + 2i) = (6 - 2i)/(6 + 2i)(6 - 2i) = (6 - 2i)/(36 - 12i + 12i + 4) = (6 - 2i)/40