Loci in the Argand diagramEdexcel A-Level Further Maths: Flashcards

What these 13 flashcards ask

What is the locus |z-a|=r?
Centre of |z+2-3i|=5?
What does |z-a|\le r represent?
What is |z-a|=|z-b|?
Cartesian equation of |z-1|=|z-i|?
What does |z-a|<|z-b| represent?
What is \arg(z-a)=\theta?
Cartesian form of \arg(z-2i)=\frac{\pi}{4}?
What is \alpha<\arg(z-a)<\beta?
How do you pick the side for an inequality region?
How do you find where two loci meet?
Convert |z-p-qi|=r to Cartesian form.
Dashed or solid boundary?

Exam questions on Loci in the Argand diagram

A point $P$ representing the complex number $z$ moves so that $|z-3+2i|=4$ .
Find the Cartesian equation of the locus of $P$ .2 marks
A point $P$ representing the complex number $z$ moves so that $|z-1|=|z-i|$ .
The point $P$ also satisfies $|z|=4$ . Find the exact possible values of $z$ .2 marks
The locus $L$ of a point $P$ representing the complex number $z$ is given by $\arg(z-2i)=\frac{\pi}{4}$ .
Describe the locus $L$ 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).