Question

For the given function u(x, y) = cos(ax) sinh(3y),(a > 0); (a) Find the value of...

For the given function u(x, y) = cos(ax) sinh(3y),(a > 0);

(a) Find the value of a such that u(x, y) is harmonic.

(b) Find the harmonic conjugate of u(x, y) as v(x, y).

(c) Find the analytic function f(z) = u(x, y) + iv(x, y) in terms of z.

(d) Find f ′′( π 4 − i) =?

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