The solutions of the equation in $z$,$|z|^2 - (z + \bar{z}) + i(z - \bar{z}) + 2 = 0$ are $(i = \sqrt{-1})$.

Let $z = x + iy$ be a complex number,$A = \{z : |z| \leq 2\}$ and $B = \{z : (1-i)z + (1+i)\bar{z} \geq 4\}$. Then which one of the following options belongs to $A \cap B$?

For the real parameter $t$, the locus of the complex number $z = (1 - t^2) + i \sqrt{1 + t^2}$ in the complex plane is

Let a complex number be $w = 1 - \sqrt{3} i$. Let another complex number $z$ be such that $|zw| = 1$ and $\arg(z) - \arg(w) = \frac{\pi}{2}$. Then the area of the triangle with vertices at the origin,$z$,and $w$ is equal to ........ .

The maximum value of the modulus of $e^{z^2}$ on the set $\{z \in \mathbb{C} : 0 \leq \operatorname{Re}(z) \leq 1, 0 \leq \operatorname{Im}(z) \leq 1\}$ is

The reflection of the complex number $(3 + 2i)$ in the straight line $z = -i \bar{z}$ is-