On an Argand diagram shade the region whose points represent complex numbers z which satisfy both the inequalities|z-4-3i|<2 and arg(z-2-i) > ¾π.

Mark scheme

Marking points from the official mark scheme (May/June 2024). The mark or mark type is shown in brackets.

1. [B1] Show a circle centre (4, 3) Allow dashes for coordinates on axes
2. [B1FT] Show a circle with radius 2. Can be implied by at least two of the points (2, 3), (6, 3), (4, 1) and (4, 5) being correct
3. [B1] Point representing (2, 1)
4. [B1FT] Show a half-line at their (2, 1) at an angle of ¾π, cutting top of circle between x = 3 and x = 5
5. [B1] Shade the correct region
6. [M1] Carry out a correct method for finding the greatest value of arg z in the correct region in (a)
7. [A1] Obtain answer 1.06, or 1.05 or 1.055 or 1.056 or 60.4° or 60.5°