Question

Which expression is a cube root of -1+i√3?

A. 3√2(cos40degrees+isin40degrees)
B. 3√2(cos120degrees+isin120degrees)
C. 3√4(cos280degrees+isin280degrees)
D. 3√4(cos320degrees+isin320degrees)

Answer 1

Put the expression into polar form:\[-1+i \sqrt{3}=2(\cos 120+i \sin 120)\]
By Demoivre's Theorem:
\[\sqrt[3]{2(\cos 120+i \sin 120}=\sqrt[3]{2}(\cos 40+i \sin 40)\]
The correct choice is A.

Answer 2

Okay, great! Thank you!

Answer 3

You're welcome :)