Maybe I just been up for too long but I just cant get why:
$$x^2+y^2=\left(3+2i\right)^2$$
and
$$x^2+y^2=25$$
give the exact same circle, why aren't the graphs different?
Shouldn't the second one mean that the radius is the distance from $(3,2i)$ to the centre which here is the origin, $\sqrt{13}$?
(From comment) I found it in this: $$\int_{|z+1−i|=1+i}\left|z^2\right|dz$$ I was just trying to visualize the contour, when I got stuck, maybe I am overlooking something basic.
You understand, don't you, that the absolute value of a complex number is a non-zero real number? "|z+ 1- i|= 1+ i" is impossible!