 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2010/paper-1/14/a/iii/solution

i

repeat with period four. Thus

i^{- 5} = i^{- 4} i^{- 1} = 1/ i = - i

, and

ℜ z = 0, ℑ z = - 1.

This negative integer power is single-valued and does not require a logarithm branch.

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