# Find all the values of (-2+2i)^(1/3)

1. Oct 4, 2011

### Jamin2112

1. The problem statement, all variables and given/known data

Find all the values of (-2+2i)1/3

2. Relevant equations

eib = cos(b) + i * sin(b)

3. The attempt at a solution

(-2+2i)1/3 = (2(-1+i))1/3 = 21/3 (√2)1/3 (eiπ(3/4 + 2m))1/3 = 21/2 (eπi)1/4 + 2m/3 = ....... Where am I going with this? I don't even know.

2. Oct 4, 2011

### jackmell

You need to use the definition:

$$u^{1/n}=|u|^{1/n} e^{i/n(\theta+2n\pi i)}$$

where $\theta$ is the argument of u

3. Oct 4, 2011

### SammyS

Staff Emeritus
Change it back to a+bi form using m=0,1,2 .