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Let z1z2, z3 zn be the complex numbers s...

Let `z_1z_2, z_3 z_n` be the complex numbers such that `|z_1|=|z_2||z_n|=1.` If `z=(sum_(k=1)^n z_k)(sum_(k=1)^n1/(z_k))` then proves that `z` is a real number `0

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