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

If $z_1$ is a point on $z\bar{z} = 1$ and $z_2$ is another point on $(4 -3i)z + (4 + 3i)z -15 = 0$, then $|z_1 -z_2|_{min}$ is (where $ i = \sqrt { - 1}$ )

If ${(\sqrt 8 + i)^{50}} = {3^{49}}(a + ib)$ then ${a^2} + {b^2}$ is

$\left| {\frac{1}{2}({z_1} + {z_2}) + \sqrt {{z_1}{z_2}} } \right| + \left| {\frac{1}{2}({z_1} + {z_2}) - \sqrt {{z_1}{z_2}} } \right|$ =

If $z=x+i y, x y \neq 0$, satisfies the equation $z^2+i \bar{z}=0$, then $\left|z^2\right|$ is equal to:

Let $z,w$be complex numbers such that $\overline z + i\overline w = 0$and $arg\,\,zw = \pi $. Then arg z equals