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    Hi all,

    Can anyone help me do this question on nth roots of unity?

    z^3 = -8, giving the answer in the form a + bi

    Thanks,
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    Write -8 in the form re^{i \theta}, where r > 0. Then, you can add 2 \pi to the argument and the number remains unchanged. Can you find three numbers in the form re^{i \theta} which all equal -8? Then, you can take the 3rd root of them using your normal laws of indices, then use Euler's identity to find them in the form a + ib.

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    -8 = 8e^{i \pi} = 8e^{3i \pi} = 8e^{5i \pi}
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    z^3 + 8 = 0. Spot the obvious root and then factorize.
 
 
 

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