 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2001/paper-1/11/a/ii/solution

i e^{i ϕ}

ϕ + π /2

2 π

. Therefore its complex logarithm has values

ln (i e^{i ϕ}) = i (ϕ + π /2 + 2 πk), k \in Z .

(- π, π]

. The unwrapped value

ϕ + π /2

is the principal imaginary part only when it already lies in that interval.

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