AS June 2025 Paper 1 Q2

2 The complex number \(3 + 5\mathrm{i}\) is a root of the quadratic equation

\[z^2 + az + b = 0\]

where \(a\) and \(b\) are real constants.

Find the other root of the equation.

Circle your answer. [1 mark]

• \(3 - 5\mathrm{i}\)
• \(3 + 5\mathrm{i}\)
• \(5 - 3\mathrm{i}\)
• \(5 + 3\mathrm{i}\)