Do not use a calculator in answering this question. The complex number $w$ is such that \(w=\

Question

Do not use a calculator in answering this question. The complex number $w$ is such that $w=\mathrm{i}-\sqrt{3}$. Find $|w|$ and $\mathrm{arg}(w)$ in exact form.[2] Represent $w$, $-w$ and $2-w$ in the same Argand diagram, illustrating clearly the geometrical relationship between them.[3] Hence, find $\mathrm{arg}(2-w)$ exactly.[2]

Accepted Answer

(i) $|w|=2$, $\arg w=\dfrac{5\pi}{6}$ (ii) $O$, $2$, $2-w$, and $-w$ form a rhombus (iii) $\arg(2-w)=-\dfrac\pi{12}$

2025 NJC P2 Q1

2025 NJC P2 Q1

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