Complex Analysis - Maths KU

C
D
(a) The horizontal strip 0 ≤ y ≤ 2
A′
B′
π z/2
w = e
(b) Image of the strip in (a)
y
2i B
C′
v
E
–1 1
A
F
D′ E′ F′
Figure 7.5 Figure for Example 4
A
(a) Image of the strip 0 ≤ y ≤ 2 under
π z/2
w = e
w =
i – z
——
i + z
D′
A′
y
–1 1
B
v
C′
B′
C D
(b) Image of the half-plane in (a) under
w =
i – z
——
i + z
Figure 7.6 Figure for Example 5
1
x
x
u
u
7.1 Conformal Mapping 395
formal mappings of the interiors of the regions shown. For example, it is clear
that the complex mapping shown in EntryE-4 is not conformal at B =0. As
a general rule, when we refer to a conformal mapping of a region R onto a
region R ′ we are requiring onlythat the mapping be conformal at the points
in the interior of R.
EXAMPLE 4 Using a Table of Conformal Mappings
Use Appendix III to find a conformal mapping from the infinite horizontal
strip 0 ≤ y ≤ 2, −∞