May/June 2026 Paper 32

Express $st$ in the form $r{\mathrm{e}}^{\mathrm{i}\theta }$, where $-\pi <\theta \le \pi$ and $r>0$.

In an Argand diagram with origin $O$, the points $A$ and $B$ represent the complex numbers $s$ and $st$ respectively. By considering the line segments $OA$ and $OB$, or otherwise, state the two geometric effects on $OA$ of multiplying $s$ by $t$.