The complex number $z$ is given by $z=k+\mathbf{i}$ where $k$ is a non-zero real number. Find the po

Question

The complex number $z$ is given by $z=k+\mathbf{i}$ where $k$ is a non-zero real number. Find the possible values of $k$ if $z=k+\mathbf{i}$ satisfies the equation ${{z}^{3}}-\mathbf{i}{{z}^{2}}-2z-4\mathbf{i}=0$. [3] For the complex number $z$ found in part (i) for which $k>0$, find the smallest integer value of $n$ such that $\left| {{z}^{n}} \right|>100$ and ${{z}^{n}}$ is real. [3]

Accepted Answer

(i) k = ±√3; (ii) n = 12

2016 ACJC P1 Q8

2016 ACJC P1 Q8

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