AS June 2022 Q1

EdexcelCurrent spec4 marksFurther Complex Numbers

1. Sketch on an Argand diagram the region defined by

\[\left\{z \in \mathbb{C} : -\frac{\pi}{4} \lt \arg(z + 2) \lt \frac{\pi}{4}\right\} \cap \left\{z \in \mathbb{C} : -1 \lt \mathrm{Re}(z) \leqslant 1\right\}\]

On your sketch

shade the part of the diagram that is included in the region
use solid lines to show the parts of the boundary that are included in the region
use dashed lines to show the parts of the boundary that are not included in the region

(4)

Argand diagram: region between the dashed half-lines from −2 at ±45° (through 2i and −2i), and between the dashed line Re(z) = −1 and the solid line Re(z) = 1, shaded; open circles at −2 and −1, filled circle at 1 — Mark scheme

Scheme	Marks	AO
Sector from ±2 or ±2i	M1	1.1b
Strip about either axis	M1	1.1b
Correct strip and sector	A1	3.1a
Fully correct	A1	2.5
	(4)
	(4 marks)

Notes