Replies:
Like most of mathematics, complex numbers were defined to provide represent-
ed prior to before. For example, without defining irrational square roots,
we would not have a way to represent the solution to the equation, x^-2 = 0.
Imaginary number, i, helps us represent a solution for x^2 + 1 = 0. Eventu-
ally, a logical way was found to connect define an algebraic system for
complex numbers and to connect them to the geometry and trigonometry of
angles.

My engineering students cannot get very far into the study of electric
circuits, etc., without understanding how complex numbers are applied there.
Complex numbers also are related to topics in advanced calculus and so have
related applications tied to calculus.

NEWTON is an electronic community for Science, Math, and Computer Science K-12 Educators, sponsored and operated by Argonne National Laboratory's Educational Programs, Andrew Skipor, Ph.D., Head of Educational Programs.