If $z_{1}$ , $z_{2}$ are two complex numbers satisfying $|\frac{z_{1} - 3 z_{2}}{3 - z_{1} \bar{z_{2}}}| = 1$ , $| z_{1} | \neq 3$ , then $| z_{2} |$ is equal to:

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Detailed Solution

$|z_{1} - 3 z_{2}| = |3 - z_{1} \bar{z_{2}}| s q u a r i n g o n b o t h s i d e s (1 - {|z_{2}|}^{2}) ({|z_{1}|}^{2} - 9) = 0 \Rightarrow |z_{2}| = 1$

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