I'm unsure of which Cauchy-Riemann law to use when I'm given either a real or imaginary function. For instance. I might be given a real function and asked to work out the imaginary part.
For instance, if I'm given the real part: $-3xy^2-2y^2+x^3+2x$ and asked to work out the imaginary, then I'd need to use the $\frac{du}{dx}=\frac{dv}{dy}$ rule rather than the $-\frac{du}{dy}=\frac{dv}{dx}$ rule before finding the imaginary part. Why is this?