May 2024
Intermediate to advanced
481 pages
17h 15m
English
Content preview from Complex Analysis
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“ca: ch_04” — 2012/3/27 — 21:16 — page 153 — #42
Complex Integration
|
153
It is positive or negative according as C travels around the point z
0
counterclockwise or clockwise,
respectively. For example, if C winds around the origin four times counterclockwise and once clockwise,
then the winding number of C around the origin is three. If C does not enclose the point z, then
η
(
C, z
0
)
= 0. Some closed contours with their winding numbers are given in Figure 4.27.
4.10.1 Properties of Winding Number
If C is a closed contour and z
0
is a point not on C, then
(i) η
(
C, z
0
)
= η
(
C
1
, z
0
)
+η
(
C
2
, z
0
)
, where C
1
and C
2
are two closed contours such that C = C
1
+C
2
(ii) η
(
−C
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