Ask A Scientist Mathematics Archive

Author:      charles l paulk
What are imaginary numbers used for?  What are some of their practical
applications?

Response #:  1 of 2
Author:      tee
"Practical" is often in the eye of the beholder.  From the perspective of
algebra, complex numbers give us a complete system for finding the roots of
polynomials.  Since numerous applications are based on polynomial models in
theory, complex numbers play a part in all of these.  For example, in
electrical engineering we find complex roots in circuit theory where the
polynomial is part of the model equation for simple circuits.  Alternating
current relates to complex root cases in the polynomial model.  In mechani-
cal engineering, the same type of model relates to vibrations with wavelike
results connected to the complex root cases.

Response #:  2 of 2
Author:      asmith
And in physics, it turns out quantum mechanics uses complex numbers for just
about everything - the wave functions of particles have a complex amplitude,
including a real and "imaginary" part, and both are essential.