de-moivres-theorem

De Moivre’s theorem

What is de Moivre’s theorem?

• de Moivre’s theorem can be used to find powers of complex numbers

• It states that for

  • Where

    • z ≠ 0

    • r is the modulus, |z|, r ∈ ℝ⁺

    • θ is the argument, arg z, θ ∈ ℝ

    • n ∈ ℝ

• In Euler’s form this is simply:

  • 

• In words de Moivre’s theorem tells us to raise the modulus by the power of n and multiply the argument by n

• In the formula booklet de Moivre’s theorem is given in both polar and Euler’s form:

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