this calculation maybe help you:
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: