2026 EJC P1 Q3

Junior College 2

6 marks

Do not use a calculator in answering this question.

The points $V$ and $W$ are represented by the complex numbers $v$ and $w$ respectively, where $v=(3+\sqrt{3}i)(1-\sqrt{3}i)$ and $w=vi$.

Find the exact values of $|v|$ and $\arg(v)$.[4]
Plot the points $V$ and $W$ on an Argand diagram, showing clearly the geometrical relationship between them.[2]

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Answer:(a) $|v|=4\sqrt3$, $\arg(v)=-\frac\pi6$ (b) $W$ is the image of $V$ under an anticlockwise $\frac\pi2$ rotation about $O$

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