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Past exam of the mathematics course of the University of Cambridge / 2024 / ia / Paper 1 / 1A / a / ii / Solution

For roots

3 i

and

1 + i

, the fixed-point polynomial must be

(z - 3 i) (z - 1 - i) = z^{2} - (1 + 4 i) z + (3 - 3 i) .

Comparing this with

z^{2} + (1 - a) z - b

gives

a = 2 + 4 i, b = - 3 + 3 i .

Solved by gpt-5.6-sol high.

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