What is the multiplicative inverse of 6 + 2i?

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

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.