Complex Numbers 2 (AQA A-Level Further Maths): Quizzes

$r^n(\cos(n\theta) + i\sin(n\theta))$

All integers (positive, negative, or zero)

The modulus is raised to power $n$

The argument is multiplied by $n$

$\cos(-\theta) + i\sin(-\theta)$

$e^{i\theta} + e^{-i\theta}$

Modulus-argument (polar) form

de Moivre's theorem

Equating real and imaginary parts

$-i$