AS June 2022 Paper 1 Q4

4 The complex numbers \(w\) and \(z\) are defined as

\[w = 2(\cos\alpha + \mathrm{i}\sin\alpha)\]\[z = 3(\cos\beta + \mathrm{i}\sin\beta)\]

Find the product \(wz\)

Tick (✓) one box. [1 mark]

• \(5\big(\cos(\alpha\beta) + \mathrm{i}\sin(\alpha\beta)\big)\)
• \(6\big(\cos(\alpha\beta) + \mathrm{i}\sin(\alpha\beta)\big)\)
• \(5\big(\cos(\alpha + \beta) + \mathrm{i}\sin(\alpha + \beta)\big)\)
• \(6\big(\cos(\alpha + \beta) + \mathrm{i}\sin(\alpha + \beta)\big)\)