# Complex number

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

hello..anyone can help me out??

berkeman
Mentor
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

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....

Mark44
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
$$(r(cos\theta + i sin\theta))^{1/n} = r^{1/n}(cos(\theta/n) + i sin(\theta/n))$$.