Back to Complex Numbers, Counting and Proof
Complex numbers in polar form and De Moivre's theorem
Questions at easy, medium and hard levels. Pick a level and get a fresh set every time, with instant feedback.
Learn it z = a + bi has modulus |z| = √(a² + b²) and argument θ (its angle). Polar form: z = r(cos θ + i sin θ) = re^(iθ). De Moivre: zⁿ = rⁿ(cos nθ + i sin nθ).
Example: Find (1 + i)⁸.
- r = √2, θ = 45°.
- (√2)⁸(cos 360° + i sin 360°) = 16.
Loading questions…