# Complex Numbers Question

• Apr 1st 2008, 06:02 PM
h2osprey
Complex Numbers Question
I've been having problems with this question - it's simple enough to solve, just that I don't seem to get the provided answers (which I suspect might be wrong).

Find the roots of (z - 2i)^5 = 1

root(3/2) +/- 3/2 i,
root(3) - 3/2 i
[root(3/2) - 3] + 3i

Yes apparently there are only 4 roots given, is there something seriously wrong with the answers provided?

Many thanks.
• Apr 1st 2008, 08:00 PM
ThePerfectHacker
Quote:

Originally Posted by h2osprey
I've been having problems with this question - it's simple enough to solve, just that I don't seem to get the provided answers (which I suspect might be wrong).

Find the roots of (z - 2i)^5 = 1

root(3/2) +/- 3/2 i,
root(3) - 3/2 i
[root(3/2) - 3] + 3i

Yes apparently there are only 4 roots given, is there something seriously wrong with the answers provided?

Many thanks.

Let $\displaystyle \zeta = \cos \frac{2\pi}{5}+i\sin \frac{2\pi}{5}$.
Then the solutions for z are: $\displaystyle 2i+1,2i+\zeta,2i+\zeta^2,2i+\zeta^3,2i+\zeta^4$.
• Apr 1st 2008, 08:15 PM
h2osprey
Yup I got those answers too - I'm assuming the provided answers are wrong then?
• Apr 2nd 2008, 06:48 AM
ThePerfectHacker
Quote:

Originally Posted by h2osprey
I'm assuming the provided answers are wrong then?

They are wrong. You can just substitute them into the equation and see they fail.