 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/i/solution

The point has positive real part and negative imaginary part. Its complex modulus is

1 + 3 = 2

, and its principal complex argument is

- π /3

. Hence

∣ z ∣ = 2, ar g z = - \frac{π}{3} + 2 πk, k \in Z .

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