Standard +0.3 This is a standard complex numbers locus question requiring students to sketch two familiar conditions: an argument inequality (sector from a point) and a modulus inequality (circle centered at origin). While it involves Further Maths content, it's a routine application of well-practiced techniques with no problem-solving or novel insight required, making it slightly easier than average.
The region \(R\) of an Argand diagram is defined by the inequalities
$$0 \leqslant \arg(z + 4\mathrm{i}) \leqslant \frac{1}{4}\pi \quad \text{and} \quad |z| \leqslant 4.$$
Draw a clearly labelled diagram to illustrate \(R\). [4]
The region $R$ of an Argand diagram is defined by the inequalities
$$0 \leqslant \arg(z + 4\mathrm{i}) \leqslant \frac{1}{4}\pi \quad \text{and} \quad |z| \leqslant 4.$$
Draw a clearly labelled diagram to illustrate $R$. [4]
\hfill \mbox{\textit{Pre-U Pre-U 9795 Q1 [4]}}