The complex numbers $z_1, z_2, z_3$ are the vertices of a triangle. Then the complex numbers $z$ which make the triangle into a parallelogram are

If $a$ is a complex number and $b$ is a real number,then the equation $\bar{a}+a+b=0$ represents $a$ as a locus of points in the complex plane,which is a:

The point $z$ in the Argand plane moves such that $\operatorname{Re} \left( \frac{iz + 1}{iz - 1} \right) = 2$. Then the locus of $z$ is:

$P$ is a point denoting $z$ in the Argand diagram. If $\frac{z-i}{z-1}$ is always purely imaginary,then the locus of $P$ is

Let $A$ and $B$ represent $z_1$ and $z_2$ in the Argand plane and $z_1, z_2$ be the roots of the equation $Z^2+pZ+q=0$,where $p, q$ are complex numbers. If $O$ is the origin,$OA=OB$ and $\angle AOB=\alpha$,then $p^2=$

Let $z=x+iy$ be a complex number with $x, y \in \mathbb{Z}$. Then,the area (in sq units) of the rectangle whose vertices are the roots of the equation $\bar{z} \cdot z^3+z \cdot \bar{z}^3=350$ is