Let $z_{1}$ be a complex number with $\left| z_{1} \right| = 1$ and $z_{2}$ be any complex number, then $\left| \frac{z_{1} - z_{2}}{1 - z_{1}z_{2}} \right|$is equal to

Question

Dr. Abubacker · Accepted Answer

(b)
We have, $\left| z_{1} ight| = 1$
$	herefore\ \ \ \ \ \left| \frac{z_{1} - z_{2}}{1 - z_{1}z_{2}} ight| = \frac{|z_{1} - z_{2}|}{|z_{1}\overline{z_{1}} - z_{1}z_{2}|}\ \ \ \ \ \ \ \ \ \ \ \ \ \lbrack\because\ \ 1 = z_{1}\overline{z_{1}}brack$
$= \frac{|z_{1} - z_{2}|}{\left| z_{1} ight||\overline{z_{1}} - z_{2}|} = \frac{1}{|z_{1}|} = 1$

Q. Let $z_{1}$ be a complex number with $\left| z_{1} \right| = 1$ and $z_{2}$ be any complex number, then $\left| \frac{z_{1} - z_{2}}{1 - z_{1}z_{2}} \right|$is equal to

Explanation

Reviewed by Dr. Abubacker

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