# Thread: Complex Numbers Question

1. ## 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

The answers given are
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.

2. 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

The answers given are
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: $\displaystyle 2i+1,2i+\zeta,2i+\zeta^2,2i+\zeta^3,2i+\zeta^4$.

3. Yup I got those answers too - I'm assuming the provided answers are wrong then?

4. 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.

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