 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2021/paper-1/11/a/i/solution

Expand the square using

i^{2} = - 1

(\frac{1}{2} + 2 i)^{2} = \frac{1}{4} + 2 i - 4 = - \frac{15}{4} + 2 i .

Re = - \frac{15}{4}, Im = 2.

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