(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

If [tex]z=6e^{3i}[/tex] then find the exact answer for [tex]Re(z^4)[/tex]

3. The attempt at a solution

What I'm having trouble with is the fact that it's not in the usual form [tex]z=re^{i\theta}[/tex] where [itex]\theta[/itex] is some multiple of [itex]\pi[/itex]. So I guess in a way I'm dealing with a not so nice answer.

Anyway, [tex]z^4=6^4e^{12i}[/tex]

Now restrict the radian angle between [tex]-\pi<\theta\leq \pi[/tex] we take away [itex]4\pi[/itex]. So our angle is now [itex]12-4\pi[/itex].

For Re(z^{4}) I suppose we take [tex]6^4cos(12-4\pi)[/tex]

Is this the exact answer I'm looking for?

Oh and while I was working on this, I tried to go down this road and can't figure out why it's wrong:

[tex]e^{3i}=\left(e^{2\pi i}\right)^{\frac{3}{2\pi}}=1^{\frac{3}{2\pi}}=1[/tex]

Of course this is not correct since the answer to the original expression is not 1. May anyone shed some light on this?

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# Homework Help: Complex numbers

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