 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/ii/solution

e^{iπ /2} = i

and

2 e^{iπ /4} = 1 + i

. Thus

z = 1 + 2 i

lies in the first quadrant, giving

∣ z ∣ = 5, ar g z = arctan (2) + 2 πk, k \in Z .

Its principal argument is approximately

1.10715

 New to topics? Read the docs here!