Complex Powers (De Moivre)
Powers and roots of complex numbers
z^(1/n) = r^(1/n)·cis((θ + 2πk)/n), k = 0…n−1
z in polar form
1 ∠ 0°
Modulus |z|
1
The 3 nth roots
- w₀ =1(1 ∠ 0°)
- w₁ =-0.5 + 0.866i(1 ∠ 120°)
- w₂ =-0.5 − 0.866i(1 ∠ -120°)
Powers and roots of complex numbers