M. Sc. Complex Analysis
13 videos • 149 views • by Doctor of Mathematics
1
Find the image of the circle |z-5|=5 under Mobius transformation w=z/z+1.
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2
Find the analytic function of which the real part is e^-x[(x^2-y^2)xcosy+2xysiny]
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3
Show that |z|^2=z.z̄
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4
Use Cauchy's integral formula to evaluate ∫(z^2+1)/(z^2-1)dz Where C has radius 1 with centre at z=1
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5
Consider the transformation w=2z and determine the region R' of w-plane into which the triangular re
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6
Find five terms in the Lauren's expansion of 1/z(e^z-1) for the region |z| greater than 0 and less
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7
find the billinera transformation of the points which maps the points -1,0,1 onto the points 0,i, 3i
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8
Use Cauchy's integral formula to evaluate z/(z^2-3z+2)dz where C is a circle |z-2|=1/2.
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9
∫e^z/z^2(z+1)^3dz,C: |z|=2
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10
Show that the function f(z)=x-iy is not analytic at any point.
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11
Find all the roots of the equation x^5-1=0.
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12
Expand f(z)=1/(z+1)(z+3) in a Laurent's series valid for the regions (i) 1 less than|z| leas rhan 3
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13
Evaluate ∫z^2+6z-1/(z-4)dz over the closed curve C ,where C is the circle|z|=5.
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