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A function \(f\) is defined on the complex numbers by \(f(z) = (a+bi)z,\) where \(a\) and \(b\) are positive real numbers. Each point in the image of \(f\) is equidistant from the point \(z\) and the origin. Given that \(|a+bi| = 8,\) find \(a\) and \(b.\)

 Dec 15, 2019
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Using the distance conditions, a + bi works out to 4 + 8i, so a = 4 and b = 8.

 Dec 16, 2019

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