who know how to convert z/(z^2+9) to z/(z+3i)/(z-3i)?i really do not have any idea how the book convert it.
If you don't see it, do it backwards and FOIL it out. Otherwise:
$\displaystyle x^2 + 9 = x^2 - (-9) = (x + \sqrt{-9})(x - \sqrt{-9}) = (x + 3i)(x - 3i)$