 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2011/paper-1/17/a/iii/solution

Write

1 + i = 2 e^{iπ /4}

and multiply the phases:

z = 2 e^{i (π /4 + π /6)} = 2 e^{5 πi /12} .

Therefore

∣ z ∣ = 2, ar g z = \frac{5 π}{12} + 2 πk, k \in Z .

The displayed representative already lies in the principal argument interval.

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