Complex Analysis - Math 427
Winter 1996
Homework
Here are the pictures we looked at in class.
If the pictures look funny, read the paragraph at the end of this
page, and/or send me a message.
The complex plane is colored using a spectrum of colors to denote the
argument of a point, and shading to denote the modulus. The origin is
black, infinity is white, and positive numbers are red.
In the pictures below, a point z is given the same color as the image
f(z) in the standard coloring. The black points are zeros of f, the
white points are poles, and f is positive at the red points.
functions:
Picture from lecture on Newton iteration.
Local behavior of rational functions: an
example
A typical example of an essential singularity:
exp(1/z)
A linear fractional transformation:
i(z-1/3)/(1-z/3)
Solution to quiz #3:
Please note that if you are using
too many colors on your screen for other applications, these pictures
will not look right. Some other applications can ruin your color table
as well. In this case, you may need to log off, reset the server and
try again. A better way to resolve this problem is to run netscape with
the install option. On our system it is:
This will run netscape with a private colormap. The colors will be
correct, so long as the cursor is in the netscape window. I prefer the
latter option, since the pictures always look better. If there are
extraneous horizontal lines in your pictures and you are using
netscape, choose refresh under View to get rid of them.
These pictures were drawn using an X-11 graphics program
written by my (former) graduate
student Mike Stark.
ADDENDUM: If you can get onto one of the math department
computers, you can run Mike Stark's program by typing the command
~marshall/PUBLIC/starkcolor/xcr1
Got a function you'd like to see?
drop by my office:
Last revised on: March 2, 1996
Standard coloring of the plane
z^2
z^3 - 2z + 2
exp(z)
(z+1/z)/2
tan(z)
