De Moivre's theorem for JEE

Formula

\([r(\cos\theta+i\sin\theta)]^n=r^n[\cos(n\theta)+i\sin(n\theta)]\)

Variables: \(r\ge 0,\ \theta\in\mathbb R,\ n\in\mathbb Z\)

Conditions: For negative \(n\), require \(r\neq 0\)

Powers of complex numbers and trigonometric identities.