The shaded region on the Argand diagram shows points representing complex numbers z defined by two inequalities. The shaded region is bounded by a circle and a line parallel to the real axis. The boundaries of the region are included in the shaded region. [Figure 3.1]

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2025). The mark or mark type is shown in brackets.

1. [B1] Obtain Im (z) < -1 Condone strict inequalities throughout (a).
2. [M1] Obtain answer of the form |z-a|<b Accept equation or any inequality sign. a = ± 2 ± i and b = 3, e.g. |z + 2-i| = 3 or |z + 2-i|>3.
3. [A1] Accept |z +2-i|≤3 as final answer. Do not ISW.
4. [M1*] Identify the coordinates of correct point (-2-√5,-1), if correct. From solving (x + 2)² + (y + 1)² = 3² (or = 3) with y = -1, or attempt to get 2 + √5 using a right-angled triangle.
5. [DM1] Carry out a correct method for finding the greatest value of |z|
6. [A1] Obtain answer 4.35 or √10+4√5 AWRT 4.35, e.g. 4.3525...