The equation $\arg \left(\frac{z-1}{z+1}\right)=\frac{\pi}{4}$ represents a circle with:

Let $z=x+iy$ be a complex number,where $x$ and $y$ are integers and $i=\sqrt{-1}$. Then the area of the rectangle whose vertices are the roots of the equation $z\bar{z}^3+\bar{z}z^3=350$ is

Let the locus of a point $z$ in the Argand plane satisfying the condition $\operatorname{Re}(z^2)=4$ be $C_1$ and the locus of $z$ satisfying the condition $\operatorname{Im}(z^2)=4$ be $C_2$. Then the number of common points of the two curves $C_1$ and $C_2$ are

Let $z_{1}$ and $z_{2}$ be two imaginary roots of $z^{2}+pz+q=0$, where $p$ and $q$ are real. The points $z_{1}, z_{2}$ and the origin form an equilateral triangle if

If $|z - 2|/|z - 3| = 2$ represents a circle,then its radius is equal to

Let $z \neq -i$ be any complex number such that $\frac{z - i}{z + i}$ is a purely imaginary number. Then $z + \frac{1}{z}$ is