Enter these expressions as Google searches if you want them evaluated. For example, a search for i^i will get the response i^i = 0.207879576. In fact, i^i and i^-i are real numbers, so it makes sense to ask which is greater. But i^(i^i) and i^(pi/2) are complex. As pickslides points out, there is no natural sense in which one is greater than the other.
October 12th 2010, 12:58 AM
Originally Posted by pickslides
Can complex numbers be ordered?
Yes, e.g. by the lexiographic order. However, there is no ordered complex field.