Loci and regions in the Argand diagramEdexcel International A Level Further Maths: Flashcards

What these 13 flashcards ask

What does |z-a| represent?
Locus of |z-a|=b?
Centre of |z-3+4i|=5?
Locus of |z-a|=|z-b|?
Locus of |z-a|=k|z-b| with k\ne1?
Locus of \arg(z-a)=\beta?
Locus of \arg\frac{z-a}{z-b}=\beta?
When is the arc of \arg\frac{z-a}{z-b}=\beta a semicircle?
Region |z-a|\le b?
Region |z-a|\le|z-b|?
Greatest value of |z| on a circle |z-a|=b?
Cartesian form of |z-2|=|z+4i|?
Cartesian form of |z+3|=\frac12|z-6|?

Exam questions on Loci and regions in the Argand diagram

The complex number $z$ satisfies $|z-3+4i|=5$ .
Find the greatest value of $|z|$ for points on the locus.2 marks
The complex number $z=x+iy$ satisfies $|z-2|=|z+4i|$ .
Find, in terms of $x$ and $y$ , the inequality satisfied by points in the region $|z-2|\le|z+4i|$ .2 marks
The complex number $z$ satisfies $\arg(z-2+i)=\frac\pi3$ , and $L$ is the locus of $z$ .
Describe $L$ geometrically, and find its Cartesian equation.3 marks

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).