Explanation

(c)
Given, $\left| z_{1} \right| = \left| z_{2} \right| = \ldots\left| z_{n} \right| = 1$
$\Rightarrow \ \ \ \left| z_{1} \right|^{2} = \left| z_{1} \right|^{2} = \ldots\left| z_{n} \right|^{2} = 1$
$\Rightarrow \ \ \ z_{1}\overline{z_{1}} = z_{1}\overline{z_{2}} = \ldots = z_{n}\overline{z_{n}} = 1$
$\Rightarrow \ \ \ \overline{z_{1}} = \frac{1}{z_{1}},\ \ \ \overline{z_{2}} = \frac{1}{z_{2}},\ \ldots.\overline{z_{n}} = \frac{1}{z_{n}}$ …(i)
Now, $|z_{1} + z_{2} + ... + z_{n}|$
$= \left| \overline{z_{1} + z_{2} + ... + z_{n}} \right| = |\overline{z_{1}} + \overline{z_{2}} + \ldots + \overline{z_{n}}|$
$= |\frac{1}{z_{1}} + \frac{1}{z_{2}} + ... + \frac{1}{z_{n}}|$ [using Eq. (i)]