Math Problem Solver

Of course! Here are the mathematical problems you provided:

### (a) Determine an analytic function whose real part is

\[ e^{2x}(x \cos 2y - y \sin 2y) \]

### (b) Solve the equation

\[ z^2 + (2i - 3)z + 5 - i = 0 \]

### (c) Show that

\[ u(x,y) = 2x - x^3 + 3xy^2 \]

is harmonic and find a harmonic conjugate of \( u(x,y) \).

These are the sums. Let me know if you need detailed solutions or further assistance with any of them!