Biology Reference
In-Depth Information
234
COMPLEX VARIABLE
The complex variable is usually represented by z = x + i y, where i = (-1)
1/2
.
A function of complex variable, f(z), is said to be regular or analytic in a
region of the complex plane, if its derivative exists (see, for example,
Carrier
et al.,
1966). The complex plane has a horizontal or real axis
denoted by x, and a vertical or imaginary axis denoted by y. The most
important theorem of complex variable is the Cauchy integral theorem
(Knopp, 1943):
for a contour which encloses a region where f(z) is analytic. The arrow
indicates that the integration is in the counter-clockwise direction (Fig. A-3).
Figure A-3.
Contour integral in the complex plane.
