MHB Hcc8.11 change each to complex form and find product

[karush]

$\tiny{hcc8.11}$
$\textsf{Find product $(1+3i)(2-2i)$}\\$

$8 + 4i$
$\textsf{Then change each to complex form and find product. with DeMoine's Theorem}$

$\textit{ok looked at an example but ??}

 

[Greg]

What you're asking is not clear. Can you quote directly from your source? Do you mean "DeMoivre's theorem"?

 

[karush]

basically yes
but this got answered

it was on a hand out which was hard to read with little information.

 

[HallsofIvy]

You probably should not use the phrase "complex form" here. These are complex number which are typically written in one of two forms, "Cartesian form", which is what you have, and "Polar form", "r(cos(\theta)+ i sin(\theta))" or (an engineering notation) "r cis(\theta)". For "a+ bi", r= \sqrt{a^2+ b^2} and \theta= tan^{-1}(b/a) (as long as a is not 0. If a= 0 \theta= \pi/2 (if b> 0) or \theta= -\pi/2 if b< 0). if a=b= 0, r= 0 and \theta can be anything.