If {z_1}, {z_2}, {z_3} are complex numbers su | vedclass

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(A) Given that $|{z_1}| = |{z_2}| = |{z_3}| = 1$. Since $|{z_i}| = 1$,we have $|{z_i}|^2 = {z_i} \overline{z_i} = 1$,which implies $\frac{1}{z_i} = \o

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Equal to $1$

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(A) Given that $|{z_1}| = |{z_2}| = |{z_3}| = 1$. Since $|{z_i}| = 1$,we have $|{z_i}|^2 = {z_i} \overline{z_i} = 1$,which implies $\frac{1}{z_i} = \overline{z_i}$ for $i = 1, 2, 3$. Given $\left| \frac{1}{z_1} + \frac{1}{z_2} + \frac{1}{z_3} \right| = 1$. Substituting $\frac{1}{z_i} = \overline{z_i}$,we get $|\overline{z_1} + \overline{z_2} + \overline{z_3}| = 1$. Using the property of conjugates $|\overline{z}| = |z|$,we have $|\overline{z_1 + z_2 + z_3}| = |z_1 + z_2 + z_3| = 1$. Therefore,$|{z_1} + {z_2} + {z_3}| = 1$.

If ${z_1}, {z_2}, {z_3}$ are complex numbers such that $|{z_1}| = |{z_2}| = |{z_3}| = \left| \frac{1}{z_1} + \frac{1}{z_2} + \frac{1}{z_3} \right| = 1$,then $|{z_1} + {z_2} + {z_3}|$ is

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