Category:Examples of Use of Equation for Perpendicular Bisector of Two Points in Complex Plane

This category contains examples of use of Equation for Perpendicular Bisector of Two Points in Complex Plane.

Let $z_1, z_2 \in \C$ be complex numbers.

Let $L$ be the perpendicular bisector of the straight line through $z_1$ and $z_2$ in the complex plane.

Parametric Form $1$

$L$ can be expressed by the equation:

$z - \dfrac {z_1 + z_2} 2 = i t\paren {z_2 - z_1}$

or:

$z = \dfrac {z_1 + z_2} 2 + i t\paren {z_2 - z_1}$

This form of $L$ is known as the parametric form, where $t$ is the parameter.

Parametric Form $2$

Equation for Perpendicular Bisector of Two Points in Complex Plane/Parametric Form 2

Standard Form

$L$ can be expressed by the equation:

$\map \Re {z_2 - z_1} x + \map \Im {z_2 - z_1} y = \dfrac {\cmod {z_2}^2 - \cmod {z_1}^2} 2$