Hmm, I hadn't really considered that. Can Matlab and/or the TI-89 do such magic?
I have no idea. Mathematica + Alpha can, Maple can. But my reason for suggesting it is mostly that if you can do that relatively quickly, all the trig functions come free (Euler's identity). z^x, for z in C and x in R is obviously easy. x^z is the more applicable one, and I assume if you can do the latter, z₁^z₂ should be doable as well.
And some of the basic results from complex analysis (residues, and the Cauchy-Riemann theorem) would be really helpful to have available in a handheld CAS.
heck, even the TI-83+ series can at least do exponentiation on the complex plane.