Trigonometry math help?!!?

Question

I have a test tomorrow so I really need to know how to do this!!
Use DeMoivre's Theorem to find the indicated power of the comples number. Express the result in standard form.

(1+i)^3.the answer in the back of the book says its -2+2i

I don't get how they got that!! Please help

I need to know how to do it with the formula because I can't multiply all of it what if it is (1+i)^12 -it would take forever to multiply...but thanks

Answer 1

(1+i)^3 = (1+i) (1+i) (1+1)
(1+2i-1) (1+i)
(2i) (1+i)
(2i-2)