If $|z - 3 - 4i| = 4$,where $i = \sqrt{-1}$,then the maximum possible value of $|z|$ is:

If the area of the triangle formed by the points $z, z + iz$ and $iz$ on the complex plane is $18$,then the value of $|z|$ is

The area of the triangle whose vertices are represented by the complex numbers $0, z,$ and $z{e^{i\alpha }}$ $(0 < \alpha < \pi )$ is equal to:

For the real parameter $t$, the locus of the complex number $z = (1 - t^2) + i \sqrt{1 + t^2}$ in the complex plane is

The equation $z\overline{z} + a\overline{z} + \overline{a}z + b = 0$,where $b \in \mathbb{R}$,represents a circle if

If at least one value of the complex number $z = x + iy$ satisfies the condition $|z + \sqrt{2}| = a^2 - 3a + 2$ and the inequality $|z + i\sqrt{2}| < a^2$,then