Write \(i\) in exponential form: \(i = e^{i\pi/2}\).

\(i^i = \left(e^{i\pi/2}\right)^i = e^{i^2 \pi/2} = e^{-\pi/2}\)

(This uses the principal value. It is a real number, about 0.2079.)

Answer: (A) \(e^{-\pi/2}\)