Exercises: Complex Numbers, Vectors, and Functions
2.4
2002/02/13
2002/08/05
Steven
Cox
cox@rice.edu
Charlet
Reedstrom
charlet@rice.edu
Jacob
Grabczewski
jgrab@owlnet.rice.edu
Steven
Cox
cox@rice.edu
Complex Differentiation
Complex Functions
Complex Numbers
Exercises
Problems
These are exercises to practice topics covered in modules regarding complex numbers, vectors, matrices, complex functions, and complex differentiation.
Exercises
Express
z
in terms of x and/or
y.
Pending completion of assignment.
Confirm that
z
z
and
z
z
.
Pending completion of assignment.
Find the real and imaginary parts of
z
and
z.
Express your answers in terms of regular and hyperbolic
trigonometric functions.
Pending completion of assignment.
Show that
z
2
z
2
1
Pending completion of assignment.
With
z
w
w
z
for complex z and
w compute
Pending completion of assignment.
Verify that
z
and
z
satisfy the Cauchy-Riemann equations and use the
proposition to evaluate their derivatives.
Pending completion of assignment.
Submit a Matlab diary documenting your use of residue in
the partial fraction expansion of the transfer function of
B
2
0
0
-1
4
0
0
-1
2
.
Pending completion of assignment.