The conjugate of the complex number $\frac{2 + 5i}{4 - 3i}$ is

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

If ${z_1}, {z_2}, {z_3}$ are complex numbers such that $|{z_1}| = |{z_2}| = |{z_3}| = \left| \frac{1}{z_1} + \frac{1}{z_2} + \frac{1}{z_3} \right| = 1$,then $|{z_1} + {z_2} + {z_3}|$ is

If the conjugate of $(x+iy)(1-2i)$ is $(1+i)$,then

Let complex number $z$ be such that $|z - \frac{6}{z}| = 5$,then the maximum value of $|z|$ will be -

Let $\alpha$ be a fixed non-zero complex number with $|\alpha| < 1$ and $w = \frac{z-\alpha}{1-\bar{\alpha}z}$,where $z$ is a complex number. Then,