### Orthogonal Circles in the Complex Plane

This graph is a plot of parametric variations, all of which happen to be circles. The basic equation is:

*Z* = *R* +*jX* = (*c*+
*jd*)/(1-*ke^y*)

where *Z* is a complex number in the *R-X*
plane,the numerator is also a complex number, as noted, and
the parameter *y* is psi. If we vary the parameter
*k*, we get circles with centers that lie along the
line *A-B* and if we vary the parameter y, we get
circles with centers that lie along the perpendicular
bisector and pass through points *A* and *B*. The
circles are orthogonal and you will note that every crossing
is at 90 degrees.

Submitted by Paul Anderson, Power Math Associates