# Complex 5th Roots

• Feb 6th 2011, 07:53 PM
collegemath
Complex 5th Roots
Can someone please show me how to find the complex 5th roots of z=-sqrt(3)=i .
• Feb 6th 2011, 07:55 PM
mr fantastic
Quote:

Originally Posted by collegemath
Can someone please show me how to find the complex 5th roots of z=-sqrt(3)=i .

Convert to polar form. Use deMoivre's Theorem. You will find many examples of this type of question in this subforum.

If you need more help, please show all your work and say where you get stuck.
• Feb 6th 2011, 10:41 PM
Ithaka
Quote:

Originally Posted by collegemath
Can someone please show me how to find the complex 5th roots of z=-sqrt(3)=i .

Do you mean $z=-\sqrt3+i$?
Or $z=-\sqrt3-i$?

Anyway:
1. Find the modulus and argument of z (i.e. write z in polar form)

2. Use DeMoivre to calculate $\sqrt[5]{z}$= $z^\frac{1}{5}$