Math 136: Complex Variables and Integral Transforms

Homework 4



Read Sections 3.3, 3.4, 3.5, and 4.1 of Saff and Snider,
and the summary at the end of Chapter 3.

Section 3.6 shows how computations about electrical circuits become simpler when formulated in terms of complex numbers.


Do these problems from Saff and Snider:

  • Sec. 3.3, The Logarithmic Function: 1b, 3, 4, 5b, 6, 11, 16.
    (Think about 2.)
  • Sec. 3.4, Washers, Wedges, and Walls: 3, 4, 5.
  • Sec. 3.5, Complex Powers and Inverse Trigonometric Functions: 3b, 7, 10, 13.
    (Think about 4, 15a.)
    Notes for 10: The observation (sqrt(5)-2)(sqrt(5)+2)=1 helps to get the answers into the required form.
    In the book, Log z means the usual real logarithm as well as the principal complex logarithm.
  • Sec. 4.1, Contours: 1b, d, 5, 8, 10.
    (Think about 3, 11, 13, 14.)


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