D. R. Wilton ECE Dept. ECE 6382 Introduction to the Theory of Complex Variables 8/24/10
Some Applications of Complex Variables
Complex Arithmetic and Algebra A complex number z may be thought of simply as an ordered pair of real numbers ( x,y) with rules for addition, multiplication, etc. e z x y r Argand diagram z
Complex Arithmetic and Algebra, Cont’d x y z1z1 z2z2 x1x1 y1y1 x2x2 y2y2 z 1 + z 2 -z 2 z 1 - z 2
Complex Arithmetic and Algebra, Cont’d z x y r z r z*
Euler’s Formula
Application to Trigonometric Identities
Application to Trigonometric Identities, Cont’d
DeMoivre’s Theorem z x y r z
Roots of a Complex Number
Roots of a Complex Number,cont’d z x y u v w Re Im Cube root of unity