MHB Tricky complex analysis questions....

Zukias
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i.
Let f and g be functions with a pole at c. Create rules (and prove them) about how we can combine f and g at c.

and ii: Find the poles of the function :
\frac{cotz+cosz}{sin2z}

and classify these poles using part i.
 
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Do you mean what happens to c when considering f+g ?
 
ZaidAlyafey said:
Do you mean what happens to c when considering f+g ?

I think it means when functions are multiplied, added, substracted, divided etc, that's what I'm assuming anyway
 
I'll say write the Laurent expansion of f and g around the pole c and see what happens when you apply the arithmetic operations on the series.
 
A sphere as topological manifold can be defined by gluing together the boundary of two disk. Basically one starts assigning each disk the subspace topology from ##\mathbb R^2## and then taking the quotient topology obtained by gluing their boundaries. Starting from the above definition of 2-sphere as topological manifold, shows that it is homeomorphic to the "embedded" sphere understood as subset of ##\mathbb R^3## in the subspace topology.
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