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If x = √(-1), then the value of x^x is

1. e^(-π/2)
2. e^(π/2)
3. x
4. 1

Correct answer: e^(-π/2)

Solution

When x = √(-1), or i, we can express x^x as iⁱ. Using Euler's formula, i can be represented as e^(iπ/2), and raising this to the power of i results in e^(-(π/2)), which corresponds to option A.

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