Mo logo [home] [lexicon] [problems] [tests] [courses] [auxiliaries] [notes] [staff] german flag
Mathematics-Online lexicon: Annotation to

Circle in the Gaussian Plane

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z overview
The equation

$\displaystyle \vert z-a\vert = s \vert z-b\vert,\quad s\ne 1\, , $

describes a circle in the Gaussian plane. Its center is

$\displaystyle w=\frac{1}{1-s^2}a-\frac{s^2}{1-s^2}b $

and the radius given by

$\displaystyle r=\frac{s}{\vert 1-s^2\vert}\vert b-a\vert \,. $

If $ s< 1$, $ a$ is located in the interior of the circle, while $ b$ is lies on its outside, vice versa for $ s > 1$.

\includegraphics[width=10cm]{kreis_komplexe_ebene}

The circle's parametric representation is given by

$\displaystyle w + r e^{\mathrm{i}t},\quad t\in[0,2\pi) \,. $

(temporary unavailable)
[Back]
  automatisch erstellt am 19.  8. 2013