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

Expanding $(cos heta + i sin heta)^n$

$(cos heta + i sin heta)^n = cos(n heta) + isin(n heta)$

Equate real and imaginary parts

$\cos^2 \theta - \sin^2 \theta$

$2\cos \theta \sin \theta$

Solving trigonometric equations

Finding roots of complex numbers

$2, 2i, -2, -2i$

$\cos^3 \theta - 3\cos \theta \sin^2 \theta$

$3\cos^2 \theta \sin \theta - \sin^3 \theta$