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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