Trouble understanding Solutions to Problems in Precalculus Section Practice: Powers of Complex Numbers

Hello,

I am working through the precalculus  course where I got stuck in the section “Multiplying and Dividing complex numbers in polar form”, specifically “Practice: Powers of Complex Numbers”.

Attached are screenshots of the problems with part of their respective solution.

I can follow each solution until I get to the equations they came up with, which I circled in red. How did they come up with the circled equations? Are these equations in any of the Khan academy resources? 

Thank you!

~Isaac