# Homework Help: Complex numbers (2)

1. Sep 11, 2009

### string_656

hey again,

im have a problem with 1 of the questions im doing.

Z^3 = 2+2i, and it asks to solve for Z.

does it want me to actually get a number for Z? or does it simply want me to write....

z = (2+2i)^(1/3)

but ^^^^ this seems way to easy

2. Sep 11, 2009

### Repainted

Well... Using De Moivre's theorem, there are actually 3 solutions for that equation.

Because 2 + 2i can be expressed as 2$$\sqrt{2}$$ei($$\pi$$/4) = 2$$\sqrt{2}$$ei($$\pi$$/4+2k$$\pi$$).

so Z3 = 2$$\sqrt{2}$$ei($$\pi$$/4+2k$$\pi$$)

=> Z = (2$$\sqrt{2}$$ei($$\pi$$/4+2k$$\pi$$))(1/3) for any 3 consecutive values of k.

3. Sep 11, 2009

### lurflurf

Poorly written instructions perhaps. You could write Z in a+ib form.

4. Sep 11, 2009

### string_656

thanks repainted, lurflurf how could i rearange it so that its in a + ib form?

5. Sep 11, 2009

### rock.freak667

Use Euler's formula of e=cosθ+isinθ