The conjugate of complex number $\frac{{2 – 3i}}{{4 – i}},$ is

The set of all $\alpha  \in R$, for which $w = \frac{{1 + \left( {1 – 8\alpha } \right)z}}{{1 – z}}$ is a purely imaginary number, for all $z \in C$ satisfying $\left| z \right| = 1$ and ${\mathop{\rm Re}\nolimits} \,z \ne 1$,  is

Let $z$ be complex number such that $\left|\frac{z-i}{z+2 i}\right|=1$ and $|z|=\frac{5}{2} \cdot$ Then the value of $|z+3 i|$ is 

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

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