Using Argument to Determine The Nature of a Complex Number Q3

Using Argument to Determine The Nature of a Complex Number Q3

Given that \(z={{e}^{-\frac{\pi }{6}\mathrm{i}}}\), find the smallest positive integer \(n\) for \({{z}^{*}}{{z}^{n}}\) to be purely imaginary.

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Answer:\( n = 4 \)

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