Thread: Solving Analytic complex variable function. (Cauchy Riemann)?

Hello,
Can someone please show me how to answer these 2 questions:

1) Given that f(z) = u(x,y) + iv(x,y) is analytic, and u - v = (x-y)(x^2 + 4xy + y^2), determine the u(x,y) and v(x,y)

2) For f(z) = u(x,y) + iv(x,y) which is analytic, and its real part is u(x,y) = x^2 + Ay^2.
a) Determine the constant A in u(x,y).
b) Given f(0) = 0, determine the function f (z)

Thanks a load in advance. Please, I am really struggling with these problems.

Because f(z) is analytic we know that .
Now skipping the tedium in doing the partials, from the given

From those to we can get now solve for u.
Repeat this process and solve for v and adjust the answers.