Q1: TUT 0203

[Victor Ivrii]

$\renewcommand{\Re}{\operatorname{Re}}
\renewcommand{\Im}{\operatorname{Im}}$
Write (in complex number notation) the equation of the the circle through $0$, $2+2i$, and $2 - 2i$.

[Ge Shi]

Since the circle through 0, 2+2i, 2-2i,
It means that the circle through (0,0), (2,2) and (2,-2)
thus, the equation of this circle in complex form is  |z-2|=2

[Vedant Shah]

This is the circle centered at $z_0=2$ with radius 2.
In other words, it is the set of points 2 units away from $z_0 = 2$. The distance of a given point, $z$, from $z_0$ is:
$d=|z-z_0|$
Thus the equation of this circle is:
$|z-2| = 2$