Find Power of Complex Number

Section 6.6

Can you do 53 and 61 as a guide for me to do a few others? Please, do in step by step fashion.
Thank you. This is it for today. My weekend is almost over.

 

53.

(5(cos(20)+i*sin(20)))^3

=(5cos(20)+5i*sin(20))^3

=(4.7+1.7i)^3

=(4.7+1.7i)^2*(4.7+1.7i)

=(19.2 -15.98*i)*(4.7+1.7i)

=63.07+107.75i


61.
(1+i)^5

=(1+i)^2(1+i)^2(1+i)

=(2 i)(2i)(1+i)

=4i^2(1+i)

=4(-1)(1+i)

=-4(1+i)

=-4-4i

 

I will solve 2 or 3 problems did coming weekend. This means we are not going to move on in the textbook until I am satisfied.