Exercises

Key Skills

Powers of Complex Numbers

De Moivre's Theorem for powers and roots of complex numbers.

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Exercises

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Practice exam-style powers of complex numbers problems

Key Skills

Powers of complex numbers

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Now that we know how to represent complex numbers in the form reiθ, we can understand De Moivre's Theorem, which gives us a shortcut to finding powers of complex numbers:

z=reiθ⇒zn=(reiθ)n=rneinθ

And since reiθ=rcisθ:

[r(cosθ+isinθ)]n=(rcisθ)n=rneinθ=rncis(nθ)📖