Question

(1-i√3)^5 using DeMoivre's Theorem

Answer 1

hint : \(\large 1-i\sqrt{3} = 2e^{i \frac{-\pi}{3}}\)

Answer 2

\[\large \left(1-i\sqrt{3}\right)^5 = \left(2e^{i \frac{-\pi}{3}}\right)^5 = 2^5\left( e^{i \frac{-5\pi}{3}} \right)\\ = 32\left(\cos(\frac{-5\pi}{3}) + i\sin (\frac{-5\pi}{3})\right) \]

Answer 3

btw, -5pi/3 is same as pi/3
so you get \( 32\left(\cos(\frac{\pi}{3}) + i\sin (\frac{\pi}{3})\right) = 16(1+i\sqrt{3})\)

Answer 4

Thanks

Answer 5

yw