Standard +0.3 This is a straightforward multiple-choice question testing understanding of argument properties in the complex plane. Students need to visualize or calculate how reflections and coordinate swaps affect arguments, requiring only basic knowledge of complex number geometry without multi-step calculations or novel insight.
Given that \(\arg(a + bi) = \varphi\), where \(a\) and \(b\) are positive real numbers and \(0 < \varphi < \frac{\pi}{2}\), three of the following four statements are correct.
Which statement is not correct?
Tick \((\checkmark)\) one box.
[1 mark]
\(\arg(-a - bi) = \pi - \varphi\)
\(\arg(a - bi) = -\varphi\)
\(\arg(b + ai) = \frac{\pi}{2} - \varphi\)
\(\arg(b - ai) = \varphi - \frac{\pi}{2}\)
Given that $\arg(a + bi) = \varphi$, where $a$ and $b$ are positive real numbers and $0 < \varphi < \frac{\pi}{2}$, three of the following four statements are correct.
Which statement is not correct?
Tick $(\checkmark)$ one box.
[1 mark]
$\arg(-a - bi) = \pi - \varphi$
$\arg(a - bi) = -\varphi$
$\arg(b + ai) = \frac{\pi}{2} - \varphi$
$\arg(b - ai) = \varphi - \frac{\pi}{2}$
\hfill \mbox{\textit{AQA Further Paper 2 2020 Q2 [1]}}