Question

De Moivre's Theorem
((2)(sqrt3) +2i) ^-5

Answer 1

if i read this correctly, you have

\(((2)(\sqrt{3}) +2i) ^{-5} \)
\( \to 2^{-5} (\sqrt{3} +i) ^{-5} \)
\( \to 2^{-5} 2^{-5} (\dfrac{\sqrt{3}}{2} +\dfrac{1}{2}i) ^{-5} \)

then \((\cos x + i \sin x)^n = \cos (nx) + i \sin (nx)\) or \(\left( e^{ix} \right)^n = e^{inx} \) if you prefer with \(x = \pi / 6\)