AS June 2022 Paper 1 Q5
5 Show that \((2 + \mathrm{i})^3\) is \(2 + 11\mathrm{i}\) [3 marks]
| Scheme | Marks | AO |
|---|---|---|
| Expands \((2 + \mathrm{i})^3\) to produce an expression of four terms with no more than one incorrect term. Or correctly expands \((2 + \mathrm{i})^2\) to two, three or four terms equivalent to \(4 + 4\mathrm{i} + \mathrm{i}^2\) and then multiplies by \(2 + \mathrm{i}\) to produce an expression of at least three terms with no more than one incorrect term. The terms may be unsimplified. | M1 | 1.1a |
| At least one instance of \(\mathrm{i}^2\) replaced with \(-1\) or \(\mathrm{i}^3\) replaced with \(-\mathrm{i}\) PI by \(3 + 4\mathrm{i}\) | B1 | 1.2 |
| Completes a reasoned argument to show that \((2 + \mathrm{i})^3\) is \(2 + 11\mathrm{i}\) | R1 | 2.1 |
| (3 marks) |