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Perpendicular Bisector in the Gaussian Plane

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The equation

$\displaystyle \vert z-a\vert = \vert z-b\vert $

describes the perpendicular bisector of the line segment $ [a,b]$ in the Gaussian plane.

\includegraphics[width=8cm]{a_gerade_bild}

In parametric representation, this line is given by

$\displaystyle \frac{a+b}{2} + \mathrm{i}(b-a)t,\quad t\in\mathbb{R} \,. $

(Authors: Höllig/Kopf/Abele)

see also:

  automatically generated 6/11/2007