Show your working and, without using a calculator, express $\frac{i}{u}$ in the form $x + iy$, where $x$ and $y$ are real.
(ii)[4]
On an Argand diagram, sketch the loci for complex numbers $z$ that satisfy the equations $|z - u| = |z|$ and $|z - i| = 2$.
(iii)[3]
Find the argument of each complex number shown by the two intersection points of the loci in part (ii).
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Substitute $u$ into $\frac{i}{u}$, then multiply the numerator and denominator by $1+i$” …