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Let the function g be defined on the complex numbers as g(z) = (a + 2 i)z for some real value of a.

Then if g(z) is equidistant from 0 and z for all z, what is a equal to?

 Dec 19, 2019
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The given condition tells us that |g(z)| = |g(z) - z|.  We can then use this condition to show that a = 2.

 Dec 19, 2019

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