A2 June 2020 Paper 2 Q2

2 Given that \(\arg(a + b\mathrm{i}) = \varphi\), where \(a\) and \(b\) are positive real numbers and \(0 \lt \varphi \lt \dfrac{\pi}{2}\), three of the following four statements are correct.

Which statement is not correct?

Tick (✓) one box. [1 mark]

• \[\arg(-a - b\mathrm{i}) = \pi - \varphi\]
• \[\arg(a - b\mathrm{i}) = -\varphi\]
• \[\arg(b + a\mathrm{i}) = \frac{\pi}{2} - \varphi\]
• \[\arg(b - a\mathrm{i}) = \varphi - \frac{\pi}{2}\]