how do you use demoivre theorem for (-1+i)^7

Answer 1

-1+i = √2 cis 3π/4
raise that to the 7th power and you have
(√2)^7 cis 7*3π/4
(√2)^7 cis 21π/4
= 8√2 cis 5π/4
= -8-8i