Tricky complex analysis questions....

[Zukias]

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.

 

[alyafey22]

Do you mean what happens to c when considering f+g ?

 

[Zukias]

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

 

[alyafey22]

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.