Evaluate , where
is the eight like figure shown in Fig. 1
1) The contour C is the eight-shaped curve shown in Figure 1. This contour consists of two semicircles of radius 1 _________ __________ _____ _____ ________ _______ ___ __________.
____ _____ ____ _______ ______ _________ __________ _________ ________ __________ ______ ___.
______ ______ _________ _______ ___ ______ ___ ____ ___ ____.
________ ___ _________ _________ _______ ___ __________.
____ ________ ____ ______ ____ ___ _______ _________ _______ ________ __________ __________.
_____ __________ _________ _____ ___ ____ _________ _______ ________.
___ _____ ________ ________ _______ _____ ___.
_____ _________ _______ __________ _________ ______ ___.
___ ___ _____ _________ _______ _____ _____ __________ ____ __________.
_____ ____ ________ ___.
Get Full Answer on WhatsApp
Evaluate where
is the circle
.
Prove that the linear fractional transformation maps the circle
into itself. Also prove that
is conformal in
.
Evaluate , where
is the eight like figure shown in Fig. 1
If f = u + iv is entire such that ux + vy = 0 in C then show that f has the form f (z) = az + b where a, b are constants with Re a = 0
Show that there is only one linear fractional transformation that maps three given distinct points and
in the extended
plane onto three specified distinct points
and
in the extended
plane.
Expand in a Laurent series valid for i)
and ii)
Evaluate the following integrals:
i)
ii)