Working in trigonometric form and using DeMoivres Theorem fi

Working in trigonometric form and using DeMoivre\'s Theorem, find (-1 - i)^6. Write your answer in a + bi form.

Solution

(-1-i)⁶

r=sqrt(1+1)=sqrt2

theta=tan^-1(-1/-1)=5pi/4

(sqrt2(cos(5pi/4)+isin(5pi/4)))⁶

sqrt2⁶(cos(30pi/4)+isin(30pi/4))

8(0-1i)

-8i