Hi Alexander,
The case here is that you should consider that you will work not only with TestComplete but with your tested application on the same machine.
This means that while for the comfortable work with TestComplete itself as with IDE the more resolution the better (and to have dual monitor setup, as Nick mentioned, is great as well), there may be a requirement for the tested application that it must operate on the low-resolution (small) monitors. This means that you will have to run tests with low resolution and there is a chance that test(s) will fail and you will have to debug them using the same low resolution. And in this case the ability of TestComplete to work on low resolutions may appear to be very handy (if not essential).
