(i)[4]
Without a calculator, and with your working shown, write $u$ in the form $x + iy$, where $x$ and $y$ are real.
(ii)[3]
Sketch an Argand diagram of the locus of the complex number $z$ satisfying $|z - u| = |u|$.
Mathematics 9709 · AS & A Level · Complex numbers
Complex numbers — practice question
The complex number $u$ is specified by $u = \frac{(1 + 2i)^2}{2 + i}$.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Expand $(1+2i)^2$ to give $-3+4i$ or an equivalent expression” …
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