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 the equation, $x^{2}+b x+45=0(b \in R)$ has conjugate complex roots and they satisfy $|z+1|=2 \sqrt{10},$ then

Let $z_1$ and $z_2$ be two complex number such that $z_1$ $+z_2=5$ and $z_1^3+z_2^3=20+15 i$. Then $\left|z_1^4+z_2^4\right|$ equals-

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

Let $w$ $(Im\, w \neq 0)$ be a complex number. Then the set of all complex number $z$ satisfying the equation $w - \overline {w}z  = k\left( {1 - z} \right)$ , for some real number $k$, is

If ${z_1}{\rm{ and }}{z_2}$ be complex numbers such that ${z_1} \ne {z_2}$ and $|{z_1}|\, = \,|{z_2}|$. If ${z_1}$ has positive real part and ${z_2}$ has negative imaginary part, then $\frac{{({z_1} + {z_2})}}{{({z_1} - {z_2})}}$may be