[Radio Wrangler]

I quite regularly express frequency as a complex variable in equations representing the transfer function of a network. The roots of the equation then can be analysed fairly easily and the patterns they make relate to recognisable solutions.

For example the roots of the equation defining a butterworth filter lie on a semicircle on an Argand diagram of frequency. A Chebyshev response distorts the circle into half an ellipse. A complete cauer looks like a Chebyshev with transmission zeroes outside the half-ellipse, along the real axis.

Can I make imaginary frequencies? Not really, but putting a mundane variable as a complex number turns complex solving into pattern geometry. It is the basis of loop stability analysis, filter design and some antenna design.

It would also blow the average audiophool's mind.

David