A-LevelMathematicsComplex numbers9709/33 · Oct/Nov 2024 · Q14 Marks

The complex number z satisfies |z|= 2 and 0 ≤ argz <¦π.

(a)On the Argand diagram below, sketch the locus of the points representing z.[2]
(b)On the same diagram, sketch the locus of the points representing z².[2]

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Mark scheme

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

[B1] (a) Show an arc of a circle, centre the origin and radius 2. Only need 2 on Re(z) or 2i on Im(z) or r = 2 to show correct radius.
[B1] (a) Show an arc centre the origin for 0 < arg z < π/2 with any radius. Max B1 if sector shaded.
[B1] (b) Show an arc of a circle, centre the origin and radius 4. Only need 4 on Re(z) or 4i on Im(z) or r = 4 to show correct radius.
[B1] (b) Show an arc centre the origin for 0 ≤ arg z² < π with any radius. Max B1 if sector shaded.

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Topic: Complex numbers, A-Level Mathematics (syllabus 9709). Structured question, 4 marks.
Source: A-Level Mathematics, Oct/Nov 2024 Paper 3 Variant 3, question 1.

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