In an Argand Diagram, mark and label clearly the points ${{P}_{1}}$ and ${{P}_{2}}$represent the com

Question

In an Argand Diagram, mark and label clearly the points ${{P}_{1}}$ and ${{P}_{2}}$represent the complex numbers $z$ and ${{z}^{2}}$ respectively, where $z=\sqrt{2}+\sqrt{2}\mathrm{i}$, and ${{P}_{0}}$ represents the complex number $1+0\mathrm{i}$. Write down the modulus and argument of $z$. [2] Find the area of triangle $O{{P}_{0}}{{P}_{1}}$, where $O$ is the origin, and find the area of triangle $O{{P}_{1}}{{P}_{2}}$. [3]

Accepted Answer

(i) $|z| = 2$, $\arg z = \displaystyle\frac{\pi}{4}$; (ii) Area $\triangle OP_0P_1 = \displaystyle\frac{\sqrt{2}}{2}$ units²; Area $\triangle OP_1P_2 = 2\sqrt{2}$ units²

N1984 P1 Q3

N1984 P1 Q3

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