1. Complex Numbers

I have to find (i)^1/3 and have no idea where to begin.

This is a multiple choice question. My choices are a. Sq. root of 3/2 - 1/2i; b. -sq.rootof 3/2 + 1/2i; c. sq.rootof 3/2 + 1/2i; d.1/2 + sq.rootof 3/2i

I have tried this a few different ways and canot get any of these answers. What am I doing wrong? Thank you for your help.

2. Hello, Joanie!

I have to find $i^{\frac{1}{3}}$

This is a multiple-choice question. .My choices are:

. . $(a)\;\frac{\sqrt{3}}{2} - \frac{i}{2} \qquad(b)\;-\frac{\sqrt{3}}{2} + \frac{i}{2} \qquad(c)\;\frac{\sqrt{3}}{2} + \frac{i}{2} \qquad (d)\;\frac{1}{2}+ \frac{i\sqrt{3}}{2}$

Since it is a multiple-choice question, you can work backwards.

Cube each of the choices and see which one give you $i.$

If you do it correctly, you'll find that it is choice (c).
.