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Given z=f(x)+ig(x) where f,g:(0,1) to (0...

Given `z=f(x)+ig(x)` where `f,g:(0,1) to (0,1)` are real valued functions. Then which of the following does not hold good?
a.`z=1/(1-i x)+i1/(1+i x)`
b. `z=1/(1+i x)+i1/(1-i x)`
c. `z=1/(1+i x)+i1/(1+i x)`
d. `z=1/(1-i x)+i1/(1-i x)`

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