Modulus-Argument Form and Loci (AQA A-Level Further Maths): Flashcards

$|z| = \sqrt{a^2 + b^2}$

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

$z = r(\cos\theta + i\sin\theta)$

$a = r\cos\theta$

$b = r\sin\theta$

$|z_1||z_2|$

$\arg(z_1) + \arg(z_2)$

Circle with centre $z_1$ and radius $r$

Half-line from $z_1$ at angle $\theta$

Perpendicular bisector of segment joining $z_1$ and $z_2$