I have this z transform $$32(\frac{z(z+\frac{3}{8})}{(z-z_{1})(z-\overline{z}_{1})})$$ with $$z_{1}=\frac{1}{16} + \frac{1}{4}i$$ The problem is I am not sure how to perform a partial fraction on these, maybe a property with the conjugated ?
I should have it on form of $$32(A\frac{z}{z-z_{1}} + \overline{A}\frac{z}{z-\overline{z}_{1}})$$ What can be the value of $A$?
I think it is $\frac12+\frac7{32}i$ but I am not sure solved, is $\frac12+\frac7{8}i$