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

[Jamin2112]

Homework Statement

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

Homework Equations

e^ib = cos(b) + i * sin(b)

The Attempt at a Solution

(-2+2i)^1/3 = (2(-1+i))^1/3 = 2^1/3 (√2)^1/3 (e^{iπ(3/4 + 2m)})^1/3 = 2^1/2 (e^πi)^{1/4 + 2m/3} = ... Where am I going with this? I don't even know.

 

[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

 

[SammyS]

Homework Statement

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

Homework Equations

e^ib = cos(b) + i * sin(b)

The Attempt at a Solution

(-2+2i)^1/3 = (2(-1+i))^1/3 = 2^1/3 (√2)^1/3 (e^{iπ(3/4 + 2m)})^1/3 = 2^1/2 (e^πi)^{1/4 + 2m/3} = ... Where am I going with this? I don't even know.

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