 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2015/paper-1/11/a/ii/solution

For real

λ

∣ λ - i ∣ = λ^{2} + 1 = ∣ λ + i ∣.

The denominator is always nonzero. Hence

∣ w ∣ = \frac{∣ λ - i ∣}{∣ λ + i ∣} = 1.

Thus the real axis maps into the unit circle in the complex plane.

 New to topics? Read the docs here!