because complex viscosity is always a positive number, i don't think there is any material with negative viscosity

Yes but we always take the mod of G* or complex viscosity. My question is whether A can have positive or negative sign?

Thanks for your answer though

we don't take a positive values but its values based on experiments and calculation  has to be positive. this is only possible when A is positive, since W is always greater then and Z is also greater then zero.