How do I find the imaginary part of this function

I need to write this function as f(x,y) = u(x,y) + iv(x,y), but I can't figure out how to break it up into purely real and purely imaginary parts.

f = i * Im(z) / z²

If z = x + iy
i * Im(z) = iy
z² = (x + iy)² = x² + 2ixy - y²

So f = iy / (x² + 2ixy - y²)

And that's where I get stuck...

Multiply both the numerator and denominator by the complex conjugate of the denominator - in this case ((x² - y²) - 2ixy). This will leave you with no complex terms in the denominator and you will be able to separate terms.