Further loci and regions in the Argand diagramEdexcel A-Level Further Maths: Mind map

Exam questions on Further loci and regions in the Argand diagram

1. The locus of points $z$ in the Argand diagram satisfying $|z-1|=2|z-4|$ is a circle $C$.
   Find the greatest value of $|z|$ for points $z$ on $C$.2 marks
2. The region $R$ of the Argand diagram is defined by $\frac{\pi}{6}\leq\arg(z-1)\leq\frac{\pi}{3}$ and $\mathrm{Re}(z)\leq3$.
   Find the exact area of $R$.2 marks
3. The locus $L$ is given by $\arg\left(\frac{z-2}{z+2}\right)=\frac{\pi}{2}$.
   Show that $L$ is part of the circle $x^2+y^2=4$, stating which part, where $z=x+iy$.3 marks