 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2013/paper-1/12/b/solution

The quadratic polynomial factors as

z^{2} - (3 + i) z + (2 + i) = (z - 1) (z - 2 - i),

because the two roots sum to

3 + i

and multiply to

2 + i

. Therefore

z = 1, z = 2 + i .

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