De Moivre’s theorem (r cis θ)ⁿ = rⁿ cis(nθ) Raise the modulus to the power n; multiply the argument by n. Worked example A power via De Moivre Find (1 + i)⁸. Polar: r = √2, θ = π/4, so 1 + i = √2 cis(π/4). (1+i)⁸ = (√2)⁸ cis(8 × π/4) = 2⁴ cis(2π). = 16 cis(2π) = 16(cos2π + i sin2π) = 16(1 + 0). ✓ (1 + i)⁸ = 16.