 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/ii/solution

Square the result of part (a)(i), keeping the cross term:

(\frac{1}{2} + 2 i)^{4} = (- \frac{15}{4} + 2 i)^{2} = \frac{225}{16} - 4 - 15 i = \frac{161}{16} - 15 i .

Hence

Re = \frac{161}{16}, Im = - 15.

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