For positive integer $n$, a complex number $z$ is such that ${{\left| z \right|}^{n}}=\frac{1}{\sqrt

Question

For positive integer $n$, a complex number $z$ is such that ${{\left| z \right|}^{n}}=\frac{1}{\sqrt{2}}$. By considering the conjugate of $1+2{{z}^{2n}}$, show that $\frac{2{{z}^{n}}}{1+2{{z}^{2n}}}$ is a real number. [4]

Accepted Answer

$\frac{4\cos\theta}{k\sqrt{2}} \in \mathbb{R}$

2020 ASRJC P1 Q8 (b)

2020 ASRJC P1 Q8 (b)

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