Answer Problems 1–10 without referring back to the text. Fill in the blank or answer true/false.
- Under the complex mapping f(z) = z2, the curve xy = 2 is mapped onto the line _____.
- The complex mapping f(z) = −iz is a rotation through _____ degrees.
- The image of the upper half-plane y ≥ 0 under the complex mapping f(z) = z2/3 is _____.
- The analytic function f(z) = cosh z is conformal except at z = _____.
- 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. _____
- Is the image of the circle z − 1 = 1 under the complex mapping T(z) = (z − 1)/(z − 2) a circle or a line? _____ ...