 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2004/paper-1/9/a/v/solution

i^{i} = exp (i lo g i) = exp [- (π /2 + 2 kπ)]

. Thus every logarithmic-branch value is real and positive:

i^{i} = e^{- π /2 - 2 kπ} + 0 i, k \in Z .

e^{- π /2}

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