Specialist2026 NHT Exam 2 Section A · Q6CAS active1 mark

Describing a region of the Argand plane

Consider the Argand diagram below.

Argand diagram showing upper semicircles of radius 1 and radius 2 centred at the origin. A shaded region lies between the two arcs, bounded on the left by the positive imaginary axis (solid) and on the right by a dashed ray from the origin making an angle of π/6 with the imaginary axis.

The shaded region is best described by

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\{z: 1 < |z| \leq 2\} \cap \left\{z: \frac{\pi}{3} \leq \arg(z) < \frac{\pi}{2}\right\}

\{z: 1 < |z| < 2\} \cap \left\{z: \frac{\pi}{6} \leq \arg(z) \leq \frac{\pi}{3}\right\}

\{z: 1 \leq |z| \leq 2\} \cap \left\{z: \frac{\pi}{6} < \arg(z) \leq \frac{\pi}{2}\right\}

\{z: 1 \leq |z| \leq 2\} \cap \left\{z: \frac{\pi}{3} < \arg(z) \leq \frac{\pi}{2}\right\}

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