The complex number $z$ is such that $\left| z \right|=1$ and $\arg z=\theta $, where&nbsp

Question

The complex number $z$ is such that $\left| z \right|=1$ and $\arg z=\theta $, where $0<\theta <\frac{\pi }{4}$. Mark a possible point $A$ on an Argand diagram. Hence, mark the points $B$ and $C$ representing ${{z}^{2}}$ and $z+{{z}^{2}}$ respectively on the same Argand diagram corresponding to point $A$.[2] State the geometrical shape of $OACB$. [1]

Accepted Answer

(i) For example, take $\theta=\frac\pi6$, with $A:z$, $B:z^2$, and $C:z+z^2$ marked as shown (ii) $OACB$ is a rhombus

2017 IJC P2 Q1

2017 IJC P2 Q1

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