20 Chapter in Review Answers to selected odd-numbered problems begin on page ANS-51.

Answer Problems 1–10 without referring back to the text. Fill in the blank or answer true/false.

  1. Under the complex mapping f(z) = z2, the curve xy = 2 is mapped onto the line _____.
  2. The complex mapping f(z) = −iz is a rotation through _____ degrees.
  3. The image of the upper half-plane y ≥ 0 under the complex mapping f(z) = z2/3 is _____.
  4. The analytic function f(z) = cosh z is conformal except at z = _____.
  5. If w = f(z) is an analytic function that maps a domain D onto the upper half-plane v > 0, then the function u = Arg(f(z)) is harmonic in D. _____
  6. Is the image of the circle z − 1 = 1 under the complex mapping T(z) = (z − 1)/(z − 2) a circle or a line? _____ ...

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