Error caused by that small difference between two number is divided by a very small number

We have a situation that the difference between two complex numbers is divided by a very small complex number. For example, the complex number is Z=10E-6 + i10E-6. The difference Delta between two complex numbers is about 10E-5. However, because of the noise in these two complex numbers (noise is around 10E-3, but we do not know their specific values). So when we solve S from the equation S = Delta / Z, we got a very big S, which expanded the noise by 10E+3.

Do you know how to obtain a reasonable S (or approximate S) from the above equation?

Thanks a lot!

[Walter Roberson]

What would your code expect if the two values were identical? What if they were identical to within round off error?