### Author Topic: Q1: TUT 0203  (Read 2119 times)

#### Victor Ivrii

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##### Q1: TUT 0203
« 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 $2 - 2i$.

#### Ge Shi

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##### Re: Q1: TUT 0203
« Reply #1 on: September 28, 2018, 05:11:53 PM »
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

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##### Re: Q1: TUT 0203
« Reply #2 on: September 28, 2018, 06:03:17 PM »
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:
$|z-2| = 2$