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I was hoping some of you would give me a clue on how to solve this complex number task.

z = (1 +(√3 /2) + i/2)^24 → x=(1 +(√3 /2), y= 1/2

I think there must be some nice looking way to solve it.

My way was to calculate |z| which was equal to [√(3+2√3)]/2 → cosθ = x/|z|, sinθ= y/|z|

After usingDe Moivre's formula I got very awful result which was:

z = |z|^24 * (cos(24*θ) + i sin(24*θ))

Can you think of any better looking way to solve this ?

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# Homework Help: Complex number - calculation

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