I don't think this will work in all cases, can you post the equation in question?
To find the conjugate of a complex number, we know that if it is of the form a+ib, then the conjugate is a-ib. Now say I have a very huge expression containing complex numbers in numerators and denominators which is very tough to reduce in the form a+ib. I have to find its conjugate. Then if I replace every i by -i in the expression, will this resultant expression be the required conjugate?
I don't believe that there are any such examples. This method will always work. In fact, conjugation is an automorphism of the field of complex numbers, so it commutes with addition, multiplication and division, and also with any function defined by means of a power series with real coefficients (such as the sinh and cosh functions in the above example).