Can someone help me please?

D. Harmonic functions 1. Determine if the function u (x, y) = e(*-y ) cos(2xy) is harmonic. 2. Let u(x, y) = sinh(x ) cos(y). Find a function v(x, y) such that the function f(z) = u(x, y) + iv(x, y) is analytic. 3. f(z) = cos(z) is an analytic function. a. Write f(z) as f(z) = u(x, y) + iv(x, y). b. Is u (x, y) harmonic? Is v(x, y) harmonic? If yes, show the functions are harmonic by finding their Laplacians. c. Write the partial sum S for f(z). Find Re(S3 ) and Im(S3). d. Are Re( S3 ) and Im(S3 ) harmonic? If yes, show the functions are harmonic by finding their Laplacians