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Question

# Use DeMoivre’s Theorem to verify the indicated root of the real number. $-\frac{1}{2}(1+\sqrt{3} i)$ is a sixth root of 1

Solution

Verified
Step 1
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If the given complex number is a sixth root of $1$, its sixth power must be equal to $1$, i.e.

$\left[-\dfrac{1}{2}\left(1+\sqrt{3}i\right)\right]^6=1$

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