On an Argand diagram, sketch the locus of points representing complex numbers z satisfying |z + 3 – 2i| = 2.

Mark scheme

Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.

1. B1 Show a circle with centre -3 + 2i. [Allow for a curved figure with 'centre' in roughly the correct position. Accept marks or numbers on axes, coordinates of centre shown. B0B1 available for axes the wrong way round (and M1 A1 in part (b)).]
2. B1 FT Show a circle with radius 2 [FT centre not at the origin. Allow 'near miss' on x axis. Different scales on axes require an ellipse for B1 B1. Scales on the axes and any label of the radius must be consistent for B1 B1. Correct circle shaded scores B1 B0.]
3. M1 Carry out a correct method for finding the least value of |z| [e.g. distance of centre from origin – radius or find point of intersection of circle and 3y = -2x and use Pythagoras. If they subtract the wrong way round M0. If their diagram is a reflection or a rotation of the correct diagram, M1 A1 is available (requires equivalent work). Any other circle M0.]
4. A1 Obtain answer √13 - 2 or √17 - 4/√13 [Or exact equivalent e.g. √(17 - 26/√3) or √(36/(3√13)). Correct solution only. Allow A1 if exact answer seen and then decimal given.]