Consider the following complex variable function: f(z) = eiz z+a2 with a real and positive. Find...

     

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Consider the following complex variable function: f(z) = eiz z+a2 with a real and positive. Find the singularities of f(z), and state their order Consider the contour y given by the real axis from -R to R, and the semicircle of radius R over the upper half plane, where R>a is also real and positive. Evaluate the following integral: [2] [4] eiz dz z+a2 1 Now take the limit R , bound the integral along the semicircle, and use the previous result to prove that L COS X = a Explain why the reasoning does not apply to COS 2 [3] [1] Consider the following complex variable function: f(z) = eiz z+a2 with a real and positive. Find the singularities of f(z), and state their order Consider the contour y given by the real axis from -R to R, and the semicircle of radius R over the upper half plane, where R>a is also real and positive. Evaluate the following integral: [2] [4] eiz dz z+a2 1 Now take the limit R , bound the integral along the semicircle, and use the previous result to prove that L COS X = a Explain why the reasoning does not apply to COS 2 [3] [1]