# Complex number

1. Jun 29, 2009

### whooi

can someone help me solve this question as fasd as possible??
thx~~

determine the 3 cube roots of 3-i over 3+i giving the result in modulus argument form,express the principal root in the form a+Jb

2. Jun 29, 2009

### whooi

hello..anyone can help me out??

3. Jun 29, 2009

### Staff: Mentor

Do not bump your post after only 16 minutes. It is unreasonable to expect fast help all the time here on the PF.

Also, you must show your attempt at a solution before we can be of help. Show us how you would go about simplifying the complex fraction that you are describing....

4. Jun 29, 2009

### Staff: Mentor

First off, you're going to want to calculate (3 - i)/(3 + i), to get it in the form a + bi. After that, you should calculate the polar form of this complex number, r(cos$\theta$ + i sin$\theta$). After that, you can use DeMoivre's Formula to find a cube root, which says that
$$(r(cos\theta + i sin\theta))^{1/n} = r^{1/n}(cos(\theta/n) + i sin(\theta/n))$$.