Show that the following functions are holomorphic on their domain f(z) =z² * i / (z² - 1) , for z ≠ ±1.
a) f(z) = z² * i / (z+1)
b) f(z) = z² * i / (z-1)
c) f(z) = z² * i / z
d) f(z) = i / z