Precalculus · N-CN
De Moivre's Theorem — Powers and Roots of Complex Numbers
[r(cos θ + i sin θ)]^n = r^n(cos nθ + i sin nθ). For nth roots, there are n distinct roots spaced 2π/n apart.
PrecalculusCommon Core HSN-CN.C.9N-CNVerified correct ✓
Worked examples
Apply De Moivre's Theorem: [3(cos 3π/2 + i·sin 3π/2)]^2. Find r^n (the modulus of the result).
Answer: 9
Apply De Moivre's Theorem: [3(cos 0 + i·sin 0)]^3. Find r^n (the modulus of the result).
Answer: 27
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