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If abs(z1)= abs(z2)= ........= abs(zn...

If `abs(z_1)`= `abs(z_2)`= ........= `abs(z_n)`=1, then show that `abs(z_1+ z_2+.......+z_n)`= `abs(frac{1}{z_1}+frac{1}{z_2}+.........frac{1}{z_n})`

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