 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/i/solution

Direct substitution in the Möbius transformation gives

w (0) = \frac{- i}{i} = - 1, w (1) = \frac{1 - i}{1 + i} = \frac{( 1 - i ) ^{2}}{2} = - i .

Neither substitution meets the excluded denominator point

z = - i

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