# Math Help - de moivre's theorem complex number

1. ## de moivre's theorem complex number

can anyone explain how ro make the working above the red circle to the working in the red circle? why the author do this?

2. ## Re: de moivre's theorem complex number

Hello, delso!

They used the Distributive Property.

$(\overbrace{z^2+\tfrac{1}{z^2}}^a + \overbrace{2}^b)(\overbrace{z^2-\tfrac{1}{z^2}}^c) \;=\;\overbrace{\left(x^2+\tfrac{1}{z^2}\right)}^a \overbrace{\left(z^2-\tfrac{1}{z^2}\right)}^c + \overbrace{2}^b \overbrace{\left(z^2 - \tfrac{1}{z^2}\right)}^c$