424 CHAPTER 10 • CONFORMAL MAPPING
Find the image of the vertical strip -t < x < 0 under the mapping w = cosz.
Find the image of the horizontal strip 0 < Im (z) < ~ under w = sinh z.
Find the image of the right half-plane Re (z) > 0 under the mapping
w = Arctanz = -i i + z
2
Log-. -.
i-z- Find the image of the first qua
0, y > 0, under w = Arcsinz. - Find the image of the first qua
0, y > O, under w = Arcsin(z^2 ).
15. Show that the transformation w = sin^2 z is a one-to-one conformal mapping of the
semi-infinite strip 0 < x < ~' y > 0, onto the upper half-plane Im (w) > 0.- Find the image of the semi-infinite strip lxl < i, y > 0, under the mapping w =
Log(sinz).