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

If $z \neq 1$ and $\frac{z^2}{z-1}$ is real,then the point represented by the complex number $z$ lies:

$\sinh(ix)$ is equal to:

The area of the triangle whose vertices are complex numbers $z, iz, z + iz$ in the Argand diagram is

If $z = x + iy$ and the point $P$ in the Argand diagram represents $z$,then the locus of the point $P$ satisfying the equation $2|z - 2 - 3i| = 3|z - 2 + i|$ is a circle with centre

The set of all real values of $c$ for which the equation $z \bar{z} + (4 - 3i) \bar{z} + (4 + 3i) z + c = 0$ represents a circle is