Question

When dividing complex numbers, why do you need to multiply the numerator and denominator by the complex conjugate of the denominator?

Answer 1

You have to multiply by the complex conjugate because the denominator has to be a real number. By multiplying the complex conjugate you can transform the denominator in to a real number.

Answer 2

Explanation:

So that the denominator is a real number. I know that doesn't sound like a good reason, but it is the reason mostly by convention. You don't want complex i's floating all over the answer. There should be just one i.