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
$b^{2}-b=42$
$b^{2}+b=12$
$b^{2}+b=72$
$b^{2}-b=30$
If $0 < amp{\rm{ (z)}} < \pi {\rm{,}}$then $amp(z)-amp ( - z) = $
Let $z$ be a purely imaginary number such that ${\mathop{\rm Im}\nolimits} (z) < 0$. Then $arg\,(z)$ is equal to
Let $z$ satisfy $\left| z \right| = 1$ and $z = 1 - \vec z$.
Statement $1$ : $z$ is a real number
Statement $2$ : Principal argument of $z$ is $\frac{\pi }{3}$
$\left| {(1 + i)\frac{{(2 + i)}}{{(3 + i)}}} \right| = $
The solution of the equation $|z| - z = 1 + 2i$ is