Test Total Name Final Examination Tuesday, May 7th, 2002 Show your work. Complex Variables 3450:425/525 Dr. Norfolk
1. Give precise statements of the following : (a) The Cauchy-Goursat Theorem
4 points
(b) The Cauchy Integral Formula for Derivatives
6 poi
Test Total
Name
Final Examination
Complex Variables 3450:425/525
Due: 12:00pm, Wednesday, December 9, 2009 Dr. Norfolk
Rules:
Show your work.
Give exact answers.
Cite any references used, other than your notes.
You may not discuss this test with anyon
Test Total
Name
Final Examination
Complex Variables 3450:425/525
Due: 3:00pm, Wednesday, December 10, 2008 Dr. Norfolk
Rules:
Show your work.
Give exact answers.
Cite any references used, other than your notes.
You may not discuss this test with anyon
Test Total Name Final Examination Tuesday, December 14th, 2004 Show your work. Complex Variables 3450:425/525 Dr. Norfolk
1. Give precise statements of the following : (a) The Cauchy-Goursat Theorem
4 points
(b) The Cauchy Integral Formula for Derivatives
Test Total Name Final Examination Complex Variables 3450:425/525 May 11, 1999 Show your work. Dr. Norfolk
1. State : (a) The Cauchy Integral Formula for Derivatives
5 points
(b) The Maximum Modulus Principle
5 points
2. Let C be the contour which consists
Test Total Name Midterm Complex Variables 3450:425/525 March 15, 2002 Show your work. Dr. Norfolk
1. Write
3 in the form a + ib. (1 + i)(3 i) 5 points
2. Use Eulers formula to nd the expansions of cos 2 and sin 2 in terms of cos and sin . 5 points
3. (a)
Test Total Name Midterm Complex Variables 3450:425 March 12, 1999 Show your work. Dr. Norfolk
1. Write
5 3i in the form a + ib. (2 + i)(1 i)
10 points
2. Use the denition of ez to prove that |ez | = ex .
10 points 3. Use polar coordinates to nd the exact
Sample Questions 1. (a) Write
Complex Variables 3450:425/525 Dr. Norfolk
2+i in the form a + bi. (1 i)(1 + 2i)
(b) Use the polar/exponential form to evaluate (1 + (d) Sketch the region 1 |z + 2 i| < 2.
3i)5 in the form a + bi
(c) Use Eulers formula and de
Test Total Name Midterm October 25, 2004 Show your work. Complex Variables 3450:425/525 Dr. Norfolk
1. (a) Write
2+i in the form a + bi. (1 i)(1 + 2i)
5 points
(b) Use the polar/exponential form to evaluate (1 +
3i)5 in the form a + bi
10 points
(c) Use
Test Total
Name
Midterm Examination
Complex Variables 3450:425/525
Due: 10:00am, Friday, October 23, 2009 Dr. Norfolk
Rules:
Show your work.
Give exact answers.
Cite any references used, other than your notes.
You may not discuss this test with anyone
Test Total Name Midterm Complex Variables 3450:425/525 Dr. Norfolk October 22, 2008 Show your work. Give exact answers where possible.
1. Write the following in the form a + bi. (a) 2i . (1 + 2i)(1 3i)
10 points (b) 2 3 + 2i
5
10 points
2. (a) Show that t