The conjugate of a complex number is $\frac{1}{{i - 1}}$ then that complex number is

If  $z_1 = a + ib$ and $z_2 = c + id$ are complex numbers such that   $| z_1 | = | z_2 |=1$ and  $R({z_1}\overline {{z_2}} ) = 0$, then the pair of complex numbers $w_1 = a + ic$ and $w_2 = b + id$ satisfies

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

The amplitude of $\frac{{1 + \sqrt 3 \,i}}{{\sqrt 3 - i}}$ is

If $|z|\, = 1,(z \ne - 1)$and $z = x + iy,$then $\left( {\frac{{z - 1}}{{z + 1}}} \right)$ is

Find the real numbers $x$ and $y$ if $(x-i y)(3+5 i)$ is the conjugate of $-6-24 i$