(a) Find all singularities of the function 1 f(z) = cos(7), and determine the nature of each of these singularities (e.g. removable singularity, pole, essential singularity). Justify all of your steps. (b) Using the Residue Theorem, or otherwise, compute ² (27) dz, Sa COS where C is the positively oriented circle of radius 5 centered at z = 0. State all the theorems that you are using and justify all of your steps.

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