CAIE A-Level Mathematics A2 3.9.4 Complex Numbers Questions

Practise representing complex numbers geometrically and analysing angles, distances and loci on Argand diagrams.

Exam points

represent complex numbers and roots on Argand diagrams
use geometry of Argand diagrams to determine angles and distances
solve algebraic conditions from geometric relationships between complex points

[Maximum number: 2]

(a)

On a sketch of an Argand diagram with origin O, show points A and B representing the roots of the equation in part (a).

[ 1 ]

Show points representing the roots correctly

B1 FT

2 roots consistent with their (a) and with no errors seen on the diagram.

B0 if they only have one root or more than 2 roots Must match their scale and $1<\sqrt{3}<2$

Linear scales seen or implied.

Need some indication of scale (numbers or dashes). Scales along an axis must be approximately consistent but scales may be different on the 2 axes.

(b)

Hence show that the triangle O A B is equilateral.

[ 1 ]

Give a complete justification that the correct triangle is equilateral
Check their diagram in (b).
Possible justifications: 3 equal sides, or all angles equal
to $\frac{\pi}{3}$ , or isosceles and an angle of $\frac{\pi}{3}$ .

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CAIE A-Level Mathematics A2 3.9.4 Complex Numbers Questions question 1

Question (a)

Question (b)