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

$e^{i\theta} = \cos\theta + i\sin\theta$

$z = re^{i\theta}$

$-\pi < \theta \leq \pi$

$|z|$ (modulus)

$\arg z$ (argument)

$\frac{e^{i\theta} + e^{-i\theta}}{2}$

$\frac{e^{i\theta} - e^{-i\theta}}{2i}$

$r_1r_2e^{i(\theta_1 + \theta_2)}$

$\frac{r_1}{r_2}e^{i(\theta_1 - \theta_2)}$

Use $e^{i\theta} = \cos\theta + i\sin\theta$, then evaluate