Loci in the Argand diagramEdexcel A-Level Further Maths: Mind map

Exam questions on Loci in the Argand diagram

1. 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
2. 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
3. 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