May 2024
Intermediate to advanced
481 pages
17h 15m
English
Content preview from Complex Analysis
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“ca: ch_08” — 2012/3/27 — 21:13 — page 350 — #4
350
|
Complex Analysis
Thus, the lines x =0,y =0,x + y = 1 of the triangle OAB in z-plane are mapped, respectively, onto
the lines u =0,v = 0 and u + v = 2 to form the triangle OA
B
in the w-plane (refer Figure 8.3).
Since
|
a
|
= 2, each side of the triangle OAB gets magnified 2 times. This transformation is only
magnification.
8.2.3 General Linear Transformation
The general linear transformation
w = az + b,
(
a = 0
)
(8.1)
is a composition of transformations Z = az,
(
a = 0
)
and w = Z + b. When z = 0, this transformation is
the resultant of magnification (contraction) and a rotation, followed by translation.
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