 Solution

ID: past-exam-of-the-mathematical-methods-i-course-of-the-university-of-oxford/2015/2/solution

i

are

i (π /2 + 2 πk)

k

i^{i} = exp [- \frac{π}{2} - 2 πk], k \in Z .

Every value is positive and real. If the power is defined using the principal logarithm, the single value is

e^{- π /2}

. Keeping the logarithm branch explicit distinguishes this value from the full multivalued set.

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