Find the complex numbers that satisfy the equation

Question

I have $$|z-3i|={\sqrt{5}}, 0 < arg(z) \le {\frac{\pi}{4}}$$ I found $$x^2+(y-3)^2 = 5$$ Therefore, the circle with $y=3$ and radius ${\sqrt{5}}$. But how do I use the fact about $arg(z)$?

Answer 1

Hint:

take a picture of the circle and of the line $arg(z)=\frac{\pi}{4}$ (that is the bisector of the first quadrant in the Argand Plane). And note that this line intersect the circle in two points.

Answer 2

The argument of a complex number gives the angle to the positive real axis. Can you use this for your problem?