Question

Using De Moivre's theorem, find (-1-i)^3

Answer 1

\[(-1-i)^3=(\sqrt{2}e^{-(3/4)pi})^3\]

Answer 2

But my textbook says -8 ...

Answer 3

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

Answer 4

Using my calculator, I got (-1-i)^3 expanded as:
\[-3i ^{2}\sqrt{3}+9i ^{2}-3i \sqrt{3}+1\]
You cancel off the first and third expression, leaving behind 9i^2 and +1
this will be -8

I want to get this by using De Moivre's theorem

Answer 5

(-1-i)^3 = -(1+3i+3i^2+i^3) = -1-3i+3+i
i don't know why −3i^2√3+9i^2−3i√3+1