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]

The complex numbers u and v are defined by u=-4+2 i and v=3+i.

Prove that angle $A O B=\frac{3}{4} \pi$ .

Use angle $A O B=\arg u-\arg v=\arg \frac{u}{v}$
Obtain the given answer
Alternative method for question 8(d)
Obtain $\tan A O B$ from gradients of O A and O B and the $\tan (A \pm B)$ formula
Obtain the given answer
Alternative method for question 8(d)
Obtain $\cos A O B$ by using the cosine rule or a scalar product
Obtain the given answer

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