Question
Asked Mar 3, 2019
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z is a complex variable z=x+iy

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Show that f(z)(3i)/(22 -2z +5) has double poles at z 1 2i and a simple pole at infinity
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Show that f(z)(3i)/(22 -2z +5) has double poles at z 1 2i and a simple pole at infinity

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Expert Answer

Step 1

To analyze and classify the singular points of the given function of the complex variable z

Step 2

Now, f(z) is a rational function (quotient of two polynomials) g(z)/h(z) . So the only singularities of f(z) in the finite part of the plane occur where h(z) =0 (poles counted with multiplicity). So, solve the equation h(z)=0

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Step 3

As h(z) vanishes at these points with multiplicity two, ...

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