FP1 June 2013 (R) Q1
1. The complex numbers \(z\) and \(w\) are given by \[z = 8 + 3\mathrm{i}, \quad w = -2\mathrm{i}\]
Express in the form \(a + b\mathrm{i}\), where \(a\) and \(b\) are real constants,
(a) \(z - w\), (1)
(b) \(zw\). (2)
| Scheme | Marks |
|---|---|
| \(z - w\ \{= (8 + 3\mathrm{i}) - (-2\mathrm{i})\} = 8 + 5\mathrm{i}\) \(8 + 5\mathrm{i}\) | B1 |
| (1) |
| Scheme | Marks |
|---|---|
| \(zw\ \{= (8 + 3\mathrm{i})(-2\mathrm{i})\} = 6 - 16\mathrm{i}\) Either the real or imaginary part is correct. \(6 - 16\mathrm{i}\) | M1 A1 |
| (2) | |
| (3 marks) |