Skip to content

Salam Academy

Sign in Create account

LearnEdexcelYFM012018 specificationWFM02 · Further Pure Mathematics 2Further complex numbers

WFM02 · Module

Further complex numbers

2 subtopics≈ 85 min in total

Start the module: Polar and exponential forms Open graphing calculator

Polar and exponential forms
Write $z$ as $r(\cos\theta+i\sin\theta)$ or $re^{i\theta}$ . In these forms multiplying is easy: multiply the moduli and add the arguments. Dividing: divide the moduli and subtract the arguments.
≈ 40 min
Loci and regions in the Argand diagram
Read $|z-a|$ as "the distance from $z$ to $a$ " and $\arg(z-a)$ as "the direction from $a$ to $z$ ". Then $|z-a|=k$ is a circle, $|z-a|=|z-b|$ a perpendicular bisector, and $\arg(z-a)=\alpha$ a half-line.
≈ 45 min