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

If the vertices of a quadrilateral are $A = 1 + 2i,$ $B = -3 + i,$ $C = -2 - 3i,$ and $D = 2 - 2i,$ then the quadrilateral is:

If $|z_1 + z_2| = |z_1 - z_2|$,then the difference in the amplitudes of $z_1$ and $z_2$ is

$A$ rectangle is constructed in the complex plane with its sides parallel to the axes and its centre situated at the origin. If one of the vertices of the rectangle is $a + ib\sqrt{3}$,then the area of the rectangle is

Let the complex numbers $\alpha$ and $\left(\frac{1}{\bar{\alpha}}\right)$ lie on circles $\left(x-x_0\right)^2+\left(y-y_0\right)^2=r^2$ and $\left(x-x_0\right)^2+\left(y-y_0\right)^2=4 r^2$ respectively. If $z_0=x_0+i y_0$ satisfies the equation $2|z_0|^2=r^2+2$,then $|\alpha|=$

For any complex number $z$,the minimum value of $|z| + |z - 1|$ is