The complex number $z$ is given by \(z=\frac{{{\left( k+ka\mathbf{i} \right)}^{2}}}{{{\left( 1-a\m

Question

The complex number $z$ is given by $z=\frac{{{\left( k+ka\mathbf{i} \right)}^{2}}}{{{\left( 1-a\mathbf{i} \right)}^{2}}}$, where $a$ and $k$ are positive real numbers. Given that $\left| z \right|=3$, find the exact value of $k$.[2] Given that $\arg \left( z \right)=\frac{2\pi }{3}$, find the exact value of $a$.[3]

Accepted Answer

(i) $k=\sqrt3$ (ii) $a=\dfrac{\sqrt3}{3}$

2020 ACJC CA2 Q3

2020 ACJC CA2 Q3

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