Complex integrals
(1) let f:C----R be an analytic function such that f(1)=1. Find the value of f(3)
(2) Evaluate the integral over & of dz/ z^2 -1 where & is the circle |z-i|=2
(3)Evaluate the integral over & of (z-1/z) dz where & is the line path from 1 to i
(4) Evaluate the integral between 2pi and 0 of
e^-i@ . e ^e^i@ d@
where @=theta
(5) Show that the integral over |z|=2 of ( z/z-1)^n = 2pi ni
(1) let f:C----R be an analytic function such that f(1)=1. Find the value of f(3)
(2) Evaluate the integral over & of dz/ z^2 -1 where & is the circle |z-i|=2
(3)Evaluate the integral over & of (z-1/z) dz where & is the line path from 1 to i
(4) Evaluate the integral between 2pi and 0 of
e^-i@ . e ^e^i@ d@
where @=theta
(5) Show that the integral over |z|=2 of ( z/z-1)^n = 2pi ni
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