How do I use DeMoivre's theorem to find ${(- 3 + 3 i)}^{3}$ $(-3+3i)^3$ ?

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How do I use DeMoivre's theorem to find ${(- 3 + 3 i)}^{3}$ $(-3+3i)^3$ ?

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Answer 1 · 2015-11-03T12:40:45

I found: $z^{3} = 54 + 54 i$ $z^3=54+54i$

Explanation:

You first need to change your complex number into trigonometric form:
$z = ρ [cos (θ) + i sin (θ)]$ $z=rho[cos(theta)+isin(theta)]$
and then apply deMoivre's Theorem to get:
$z^{n} = ρ^{n} [cos (n θ) + i sin (n θ)]$ $z^n=rho^n[cos(ntheta)+isin(ntheta)]$
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How do I use DeMoivre's theorem to find ${(- 3 + 3 i)}^{3}$ $(-3+3i)^3$ ?

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How do I use DeMoivre's theorem to find ${(- 3 + 3 i)}^{3}$ $(-3+3i)^3$ ?