Toronto Math Forum
MAT3342018F => MAT334Tests => Quiz1 => Topic started by: Victor Ivrii on September 28, 2018, 04:13:59 PM

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

Since the circle through 0, 2+2i, 22i,
It means that the circle through (0,0), (2,2) and (2,2)
thus, the equation of this circle in complex form is z2=2

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:
$d=zz_0$
Thus the equation of this circle is:
$z2 = 2$