If $\alpha $ and $\beta $ are different complex numbers with $\left| {\rm{\beta }} \right| = 1{\rm{\;then\;}}\left| {\frac{{{\rm{\beta }} - {\rm{\alpha }}}}{{1 - \bar \alpha {\rm{\beta }}}}} \right|\;$ is equal to

JEE MATHEMATICS MCQ: COMPLEX NUMBERS

1 Easy

1 of 1

Application +4 | -1

\alpha

and

\beta

are different complex numbers with

\left| \mathrm{\beta } \right| = 1\mathrm{\;then\;}\left| {\frac{{\mathrm{\beta } - \mathrm{\alpha }}}{{1 - \bar \alpha \mathrm{\beta }}}} \right|\;

is equal to

View answer and explanation

Correct option: C

Option C (1) is correct because the expression simplifies to 1 using the property that |β| = 1 and |z| = |conjugate(z)|.

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{\left| {1 - i} \right|^x} = {2^x}

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z, \frac{z}{1-z^2}

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\left|\sum\limits_{r=1}^n z_r\right|

(z+a b)^3=a^3

a \neq 0

\alpha, \beta

\gamma

|\alpha-\beta|

{z^2} + {\left| z \right|^2} = 0,

z \in C

2x = - 1 + \sqrt 3 i

{\left( {1 - {x^2} + x} \right)^6} - {\left( {1 - x + {x^2}} \right)^6}