Using Argument to Determine The Nature of a Complex Number Q1

Using Argument to Determine The Nature of a Complex Number Q1

Given that \(z={{e}^{\frac{3\pi }{4}\mathrm{i}}}\), find the smallest positive real number \(n\) for \({{z}^{n}}\) to be a positive real number.

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Answer:\( n = \frac{8}{3} \)

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