If z_{1}, z_{2}, z_{3} are complex numbers su | vedclass

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(A) Given $|z_{1}|=|z_{2}|=|z_{3}|=1$. Since $|z|=1$ $\Rightarrow z\bar{z}=1$ $\Rightarrow \bar{z}=\frac{1}{z}$. Thus, $\frac{1}{z_{1}}=\bar{z}_{1}$,

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equal to $1$

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(A) Given $|z_{1}|=|z_{2}|=|z_{3}|=1$. Since $|z|=1$ $\Rightarrow z\bar{z}=1$ $\Rightarrow \bar{z}=\frac{1}{z}$. Thus, $\frac{1}{z_{1}}=\bar{z}_{1}$, $\frac{1}{z_{2}}=\bar{z}_{2}$, and $\frac{1}{z_{3}}=\bar{z}_{3}$. We are given $|\frac{1}{z_{1}}+\frac{1}{z_{2}}+\frac{1}{z_{3}}|=1$. Substituting the conjugates, we get $|\bar{z}_{1}+\bar{z}_{2}+\bar{z}_{3}|=1$. Using the property $|\bar{z}|=|z|$, we have $|\overline{z_{1}+z_{2}+z_{3}}|=1$. Therefore, $|z_{1}+z_{2}+z_{3}|=1$.

If $z_{1}, z_{2}, z_{3}$ are complex numbers such that $|z_{1}|=|z_{2}|=|z_{3}|=|\frac{1}{z_{1}}+\frac{1}{z_{2}}+\frac{1}{z_{3}}|=1$, then $|z_{1}+z_{2}+z_{3}|$ is

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