Complex Number Exponentiation

[DeanSchlarbaum]

How does one calculate a whole number (1, 2, 3,....) raised to a complex number (of the form a + bi) power? Could someone "walk me through," the process of, say, calculating 2 ^ (2 + 2i)? Is the result a "number" of the form that could/can be graphed on a complex number coordinate system? Is there a general method for these types of calculations -- of, say, doing x ^ (a + bi)? Any and all help with this aspect of math. greatly appreciated. My interest in these types of calculations comes from seeing the Reimann Zeta Function (and also the Euler Zeta Function). Dean

[stapel_eliz]

The process involves polar coordinates, etc, and isn't usually covered until you're in calculus. But you can read many nice lessons online:

. . . . .Google results for "complex powers"

Have fun!