# Homework Help: Complex numbers

1. Jan 12, 2008

### sara_87

find all complex numbers satisfying z^3=-8
i have no idea how to solve this can someone help please?
thank u

2. Jan 12, 2008

### trambolin

Think -8 as -8 + 0i... Then convert this into polar coordinates.

3. Jan 12, 2008

### sara_87

in polar coordinates it will be:
-8=8(cos0+isin0)
giving
-8=8
???

4. Jan 14, 2008

### Marco_84

i think that if you write down z=rexp(ix) would be easier...
you find three roots on the cricle with radius r=(-8)^(1/3).

bye
marco

5. Jan 14, 2008

### HallsofIvy

Are you saying you have been asked to find cuberoots and have never heard of D'Moivre's theorem? Why that's awful! Almost as bad posting a homework problem under the mathematics thread!

6. Jan 14, 2008

### Shooting Star

He actually doesn't need D'Moivre's theorem, only the three cube roots of unity.

Hi sara_87,

Have you done the complex cube roots of one in class? You know, omega, omega^2 etc.? Show some work.

7. Jan 14, 2008

### rock.freak667

Or just basic remainder and factor theorem....f(z)=z^3+8=0. But the other ways are faster.