de Moivre's Theorem (Edexcel A-Level Further Mathematics): Flashcards

Trigonometry and complex numbers

Modulus-argument form (or exponential form)

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

$r^n$

$n\theta$

$r^{1/n}\left(\cos \frac{\theta + 2k\pi}{n} + i \sin \frac{\theta + 2k\pi}{n}\right)$

$n$ distinct roots

$k = 0, 1, 2, ..., n-1$

$-8-8i$

$2$, $-1+i\sqrt{3}$, $-1-i\sqrt{3}$