Question

The principal value of \( i^i \) is:

• A. \( e^{-\pi i} \)
• B. \( e^{\pi i} \)
• C. \( e^{-\pi/2} \)
• D. \( e^{-\pi/4} \)

Hint:

The principal value of powers of complex numbers involves using logarithms and Euler’s formula to simplify expressions.

Answer 1

The Correct Option is C

The principal value of \( i^i \) can be computed by using the logarithmic representation of complex numbers. Using Euler’s formula, we find that: \[i^i = e^{-\pi/2}.\]