If $z=x+iy$ represents a point $P$ in the Argand plane, then the area of the region represented by the inequality $2 < |z-(1+i)| < 3$ is (in $\pi$)

The area of the triangle with vertices $A(z)$,$B(iz)$,and $C(z+iz)$ is

$\sinh(ix)$ is equal to

If $z$ is a complex number such that $\frac{z-i}{z-1}$ is purely imaginary,then the minimum value of $|z-(3+3i)|$ is:

Let $z$ be a complex number such that $|z + 2| = |z - 2|$ and $\arg\left(\frac{z + 3}{z - i}\right) = \frac{\pi}{4}$. Then $|z|^2$ is equal to:

If $a$ and $c$ are complex numbers and $b$ is a real number in the Argand plane,then the perpendicular distance from $c$ to the line $a \bar{z} + \bar{a} z + b = 0$ is