Moderate -0.8 This is a straightforward multiple-choice question requiring only one mark. Given a complex root of a cubic with real coefficients, students need to recognize that the conjugate 1+i must also be a root, then find the third root via sum of roots or factorization. The multiple-choice format and single mark indicate this is testing basic recall of complex conjugate root theorem rather than problem-solving ability, making it easier than average.
Given that \(1 - i\) is a root of the equation \(z^3 - 3z^2 + 4z - 2 = 0\), find the other two roots.
Tick \((\checkmark)\) one box.
[1 mark]
\(-1 + i\) and \(-1\)
\(1 + i\) and \(1\)
\(-1 + i\) and \(1\)
\(1 + i\) and \(-1\)
Given that $1 - i$ is a root of the equation $z^3 - 3z^2 + 4z - 2 = 0$, find the other two roots.
Tick $(\checkmark)$ one box.
[1 mark]
$-1 + i$ and $-1$
$1 + i$ and $1$
$-1 + i$ and $1$
$1 + i$ and $-1$
\hfill \mbox{\textit{AQA Further AS Paper 1 2020 Q2 [1]}}