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Math · Advanced Math
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5. (a) . Show that by using the substitutione 1+2cos 13 +5cos άθ can be rewritten as where C is the unit circle 5 Marks ii. Locate and classify the poles of this function and hence find the value of I 5 Marks (b) Transform the Real integral into a complex integral 2-52 (+9)(r2 + 16) integral clearly specifying the appropriate path. ii. Locate and classify the poles and find the residue of each. ii. Evaluate the integral; iv. Give 2 examples of functions which are analytic/ non analytic 4 Marks 4 Marks 2 Marks 5 Marks e) Using Complex Numbers show sinz +cos z 1 5 Marks (d) Give 2 examples of functions which are analytic/non analytic ? 5 Marks

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