2025 YIJC P2 Q2
2025 YIJC P2 Q2
Junior College 2
8 marks
Do not use a calculator in answering this question.
It is given that \(z = \sqrt{3} - \mathrm{i}\) and \(w = 2\mathrm{i}z\).
- Find the modulus and argument of \(z\).[2]
- Deduce the modulus and argument of \(w\).[2]
\(O\), \(A\), \(B\) and \(C\) represent the complex numbers \(0\), \(z\), \(z + w\) and \(w\) respectively.
- Illustrate these four points on a single diagram.[2]
- Identify the shape of the quadrilateral \(OABC\) and state its area.[2]
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Answer:(a) modulus \(2\), argument \(-\dfrac\pi6\) (b) modulus \(4\), argument \(\dfrac\pi3\) (c) \(O=(0,0)\), \(A=(\sqrt3,-1)\), \(B=(2+\sqrt3,2\sqrt3-1)\), \(C=(2,2\sqrt3)\) (d) rectangle, area \(8\text{ units}^2\)
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