Question

what happens when you multiply a radical or complex # by its conjugate?

Answer 1

The radicals or "i" cancel out.

Answer 2

can you give me an example??

Answer 3

(7+8i)(7-8i) = 49 + 64

Answer 4

= 113

Answer 5

(√5 + 3). The conjugate is (√5 - 3)
When you foil it, this is what happens.
5 - 3√5 + 3√5 - 9
5 - 9 = -4
The middle terms which carry the radical or i, cancel out.

Answer 6

This is basically a difference in squares pattern if you are familiar with it.

Answer 7

You'll notice that instead of (a-b)(a+b) becoming a^2 - b^2, you obtain a^2+b^2, as i^2 is equal to -1

Answer 8

This is also why rationalizing the denominator works.