COMPLEX ANALYSIS: Maple Worksheets, 2001
(c) John H. Mathews Russell W. Howell
mathews@fullerton.edu howell@westmont.edu

Complimentary software to accompany the textbook:

COMPLEX ANALYSIS: for Mathematics & Engineering, 4th Ed, 2001, ISBN: 0-7637-1425-9
Jones and Bartlett Publishers, Inc., 40 Tall Pine Drive, Sudbury, MA 01776
Tele. (800) 832-0034; FAX: (508) 443-8000, E-mail: mkt@jbpub.com, http://www.jbpub.com/

CHAPTER 1 COMPLEX NUMBERS

Section 1.6 The Topology of Complex Numbers

In this section we investigate some basic ideas concerning sets of points in the plane.
The first concept is that of a curve.

Definition: Curve

A curve in the complex plane is:

: for .

Example 1.22, Page 40. If and are two given points, then the straight line segment joining to is C: for .

> t:='t':x0:='x0':x1:='x1':y0:='y0':y1:='y1':z:='z':
z := t -> x0 + (x1-x0)*t + I*(y0 + (y1-y0)*t):
`Equation of a line segment:`;
`z(t) ` = z(t), ` for 0 <= t <= 1`; ` `;
`Initial point z(0) ` = z(0);
`Terminal point z(1) ` = z(1);

Extra Eample, Page 40. Find the equation of the line segment with the initial point and the terminal point .

> t:='t':x0:='x0':x1:='x1':y0:='y0':y1:='y1':z:='z':
z0 := - 3 + 2*I:
z1 := 1 + I:
x0 := Re(z0): y0 := Im(z0): x1 := Re(z1): y1 := Im(z1):
z := t -> x0 + (x1-x0)*t + I*(y0 + (y1-y0)*t):
`Equation of a line segment:`;
`z(t) ` = z0 + (z1 - z0)*t, ` for 0 <= t <= 1`; ` `;
`Initial point z(0) ` = z(0);
`Terminal point z(1) ` = z(1);

The graph for this line segment can is drawn with the plot subroutine.

> plot([evalf(Re(z(t))),evalf(Im(z(t))), t=0..1],
title=`Line segment between z0 and z1.`,
scaling=constrained, color=red,
labels=[` x`,` y`],
view=[-3.5..1.5,-1.0..3.50]);

End of Section 1.6.