If the amplitude of $z-2-3i$ is $\pi/4$,then the locus of $z=x+iy$ is

The locus of $z$ satisfying the inequality $\log_{1/3}|z + 1| > \log_{1/3}|z - 1|$ is

If $\sin \alpha + \sin \beta + \sin \gamma = 0$ and $\cos \alpha + \cos \beta + \cos \gamma = 0,$ then the value of $\sin^2 \alpha + \sin^2 \beta + \sin^2 \gamma$ is

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

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

If the point $\left(\frac{k-1}{k}, \frac{k-2}{k}\right)$ lies on the locus of $z$ satisfying the inequality $\left|\frac{z+3i}{3z+i}\right| < 1$,then the interval in which $k$ lies is