The conjugate of $\frac{{{{(2 + i)}^2}}}{{3 + i}},$ in the form of $a + ib$, is
$\frac{{13}}{2} + i\,\left( {\frac{{15}}{2}} \right)$
$\frac{{13}}{{10}} + i\left( {\frac{{ - 15}}{2}} \right)$
$\frac{{13}}{{10}} + i\,\left( {\frac{{ - 9}}{{10}}} \right)$
$\frac{{13}}{{10}} + i\,\left( {\frac{9}{{10}}} \right)$
If $z $ is a complex number of unit modulus and argument $\theta$, then ${\rm{arg}}\left( {\frac{{1 + z}}{{1 + (\bar z)}}} \right)$ equals.
Given $z$ is a complex number such that $|z| < 2,$ then the maximum value of $|iz + 6 -8i|$ is equal to-
If $arg\, z < 0$ then $arg\, (-z)\, -arg(z)$ is equal to
The amplitude of $\frac{{1 + \sqrt 3 \,i}}{{\sqrt 3 - i}}$ is
Let $S=\left\{z \in C : z^{2}+\bar{z}=0\right\}$. Then $\sum \limits_{z \in S}(\operatorname{Re}(z)+\operatorname{Im}(z))$ is equal to$......$