If `|z_1|=|z_2|=.......=|z_n|=1,` prove that `|z_1+z_2+z_3++z_n|=1/(z_1)+1/(z_2)+1/(z_3)++1/(z_n)`

Explanation

To prove that if \( |z_1| = |z_2| = \ldots = |z_n| = 1 \), then

\[ |z_1 + z_2 + z_3 + \ldots + z_n| = \frac{1}{\overline{z_1}} + \frac{1}{\overline{z_2}} + \frac{1}{\overline{z_3}} + \ldots + \frac{1}{\overline{z_n}}, \]

we can follow these steps:

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