12. If f(z) = u+ iv is an analytic function of z = x+ iy, and...

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12. If f(z) = u+ iv is an analytic function of z = x+ iy, and u – v = e" (cos y – sin y), find f(z) in terms of z. Ans: f(z) = e² +c. y}, where 13. Consider the function f u(x, y) = x², v(x, y) = y². Note that u, v satisfies the C-R equations in D, and u, Uy, Væ, Vy are also continuous in D. Prove that f is not analytic on D. Does this fact contradict the related Theorem? If not, explain why. = u + iv defined on the set D := {x + iy E C : x = 12. If f(z) = u+ iv is an analytic function of z = x+ iy, and u – v = e" (cos y – sin y), find f(z) in terms of z. Ans: f(z) = e² +c. y}, where 13. Consider the function f u(x, y) = x², v(x, y) = y². Note that u, v satisfies the C-R equations in D, and u, Uy, Væ, Vy are also continuous in D. Prove that f is not analytic on D. Does this fact contradict the related Theorem? If not, explain why. = u + iv defined on the set D := {x + iy E C : x =

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Date Page 12 Given fz utiv s an analytic function of Zxtiy and ecosy Siny UVE Now Cuv 1... View the full answer