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(B) Given $|{z_1}| = 1$ and ${z_2}$ is any complex number.Consider the expression $\left| \frac{{z_1 - z_2}}{{1 - z_1 \bar{z}_2}} \right|$.Since $|{z_

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(B) Given $|{z_1}| = 1$ and ${z_2}$ is any complex number.Consider the expression $\left| \frac{{z_1 - z_2}}{{1 - z_1 \bar{z}_2}} \right|$.Since $|{z_1}| = 1$,we have ${z_1} \bar{z}_1 = |{z_1}|^2 = 1$,which implies $\bar{z}_1 = \frac{1}{z_1}$.Substituting this into the denominator: $\left| 1 - z_1 \bar{z}_2 \right| = \left| z_1 \bar{z}_1 - z_1 \bar{z}_2 \right| = |z_1| |\bar{z}_1 - \bar{z}_2|$.Since $|z_1| = 1$,this simplifies to $|\bar{z}_1 - \bar{z}_2| = |\overline{z_1 - z_2}|$.Using the property $|\bar{z}| = |z|$,we get $|\overline{z_1 - z_2}| = |z_1 - z_2|$.Therefore,$\left| \frac{{z_1 - z_2}}{{1 - z_1 \bar{z}_2}} \right| = \frac{|z_1 - z_2|}{|z_1| |\bar{z}_1 - \bar{z}_2|} = \frac{|z_1 - z_2|}{|z_1 - z_2|} = 1$.

Let ${z_1}$ be a complex number with $|{z_1}| = 1$ and ${z_2}$ be any complex number,then $\left| \frac{{z_1 - z_2}}{{1 - z_1 \bar{z}_2}} \right| = $

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