If $\alpha$ and $\beta$ are two different complex numbers with $|\beta|=1$, then $\left | \dfrac{\beta -\alpha}{1-\bar{\alpha }\beta } \right |$ is equal to.

Let $t = \left|\cfrac { \beta -\alpha }{ 1-\overline { \alpha } \beta } \right|$

Multiply the numerator and denominator with $\overline { \beta }$

$\Rightarrow t = \left|\cfrac { 1-\alpha \overline { \beta } }{ \overline { \beta } -\overline { \alpha } } \right| = \left|\cfrac { \overline { 1- \alpha \overline { \beta } } }{ \overline { \overline{\beta} -\overline{\alpha} } } \right| = \left|\cfrac { 1-\overline { \alpha } \beta }{ \beta -\alpha } \right|=\cfrac{1}{t}$

$\Rightarrow {t}^{2} = 1$

$\Rightarrow t = 1$