I need to find and draw a set of complex numbers on complex plain with such conditions:
\begin{cases} 0 < \arg(z^4) < \pi\\ |z + 1 - i| \ge |z - 1 - i| \end{cases}
I got two points $A = (i - 1)$ and $B = (i + 1)$. I drew them on complex plane and how them I can determine set of complex numbers which satisfy equations?
And what does $\arg z$ mean?
$\arg z$ means the argument of $z$ (if you draw a line from the point to the origin, $\arg z $ is the angle from the positive $x$-axis.
$$0 < \arg z^4 < \pi \iff 0 < \arg z < \frac{\pi}{4} \quad (\textrm{the points are in an eighth of the plane contained in the first quadrant})$$
The second condition states that the distance from $z$ to $1+i$ is greater than or equal to the distance from $z$ to $-1+i$. This would be points in the left half plane including the imaginary axis.
If these are two questions, then there are two answers (above). If both conditions are to be met simultaneously, then the set of solutions is empty.
The argument of the point at the origin is undefined.