# Math Help - Trigonometry Finding the nth roots of a complex number.?

1. ## Trigonometry Finding the nth roots of a complex number.?

Trigonometry Finding the nth roots of a complex number.?

Find the nth roots of the complex number and write each of the roots in standard form.

I am trying to understand how to do this problem. but I just cannot figure out how the books answer comes up with 128 sqrt(2). The way I want to see it is 5sqrt(2). Then how does it go to 2sqrt(2)?

fifth roots of 128(-1+i) = 128sqrt(2)(cos 135 deg + i sin 135 deg)

Here is the books answer:

http://i333.photobucket.com/albums/m400/.

2. Dear robasc,

this calculation maybe help you:

$128* \sqrt[2]2 = 2^5*2^2* \sqrt[2]2 = 2^5* (\sqrt[2]2)^5 = (2* \sqrt[2]2)^5$