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

Exam questions on Loci and regions in the Argand diagram

1. The complex number $z$ satisfies $|z-3+4i|=5$.
   Find the greatest value of $|z|$ for points on the locus.2 marks
2. 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
3. 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