De Moivre’s theorem

From multiplication of complex numbers in polar form,

(r∠θ) × (r∠θ) = r2∠2θ Similarly, (r∠θ) × (r∠θ) × (r∠θ) = r3∠3θ, and so on. In general, de Moivre’s theorem states:

[r∠θ]n = rn∠nθ The theorem is true for all positive, negative and fractional values of n. The theorem is used to determine powers and roots of complex numbers.