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Complex Numbershard
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Let zzz be a complex number satisfying zn=1z^n = 1zn=1 where n=4n=4n=4. Consider the transformation f(z)=1z+2f(z) = \frac{1}{z+2}f(z)=z+21​. Which of the following represents the sum of the transformed values of all fourth roots of unity?