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if z(1),z(2),z(3),…..z(n) are complex n...

if ` z_(1),z_(2),z_(3),…..z_(n)` are complex numbers such that ` |z_(1)|=|z_(2)| =….=|z_(n)| = |1/z_(1) +1/z_(2) + 1/z_(3) +….+1/z_(n)| =1`
Then show that `|z_(1) +z_(2) +z_(3) +……+z_(n)|=1`

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To solve the problem, we need to show that if \( |z_1| = |z_2| = \ldots = |z_n| = |1/z_1 + 1/z_2 + \ldots + 1/z_n| = 1 \), then it follows that \( |z_1 + z_2 + \ldots + z_n| = 1 \). ### Step-by-Step Solution: 1. **Given Conditions**: We know that \( |z_1| = |z_2| = \ldots = |z_n| = 1 \). This means that each \( z_i \) lies on the unit circle in the complex plane. 2. **Expressing the Conjugates**: ...
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