616 ANSWERS17. The equation z = ~=~~ can be written as cz^2 + (d - a)z - b = 0, and a
quadratic equation has, at most, two distinct solutions.Section 10.3. Mappings Involving Elementary Functions: page 417
- The portion of the disk lw l < 1 that lies in the first quadrant u > 0 , v > 0.
- The horizontal strip 0 < Im(w) < 1.
- T he vert ical strip 0 < Re(w) < 1.
- The region 1 < lwl.
9. The horizontal strip 0 < lm(w) < 1r. - The portion of the upper half- plane Im(w) > 0 that lies in t he region lwl > 1.
13. z = z^2 + 1, w = z!' where the principal branch of the square root z! is
used.15. The unit disk lwl < 1.Section 10.4. Mapping by Trigonometric Functio ns: page 423- The portion of the d isk lwl < 1 that lies in t he second quadrant
Re(w) < 0 ,Im(w) > O. - T he right branch of the hyperbola u^2 - v^2 = ~.
- The region in the first quadrant u > 0, v > 0 that lies inside the ellipse
0 .,;':2 1 + sinv:,^1 =^1 and to the left of t he hyperbola u
(^2) - v (^2) =!.
- (a) ~, (b) -r.
- The port ion of tlie upper half-plane Im (w) > 0 that lies insid e the ellipse
u• v• - 1
cosh^2 b + sinh^2 b - · - The upper half-plane Im(w) > 0.
- The semi-infinite strip 0 < u < ~, v > O.
- The upper half-plane Im(w) > O.
Section 11.2. Invariance of Laplace's Equation and the Dirichlet
Problem: page 437
- 4>(x, y) = 15 - 9y.
- 4>(x,y)=5+ 11 ~ 2 lnlzl.