In an Argand diagram, with origin $$$O$$$, the points $$$A, B$$$ and $$$C$$$ represent the complex numbers $$$u, v$$$ and $$$2 u+v$$$ respectively. The complex numbers $$$u$$$ and $$$v$$$ are defined by $$$u=-4+2 \mathrm{i}$$$ and $$$v=3+\mathrm{i}$$$. Prove that angle $$$A O B=\frac{3}{4} \pi$$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_m21_qp_32 Year：2021 Question No：8(d)

Answer:

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

Knowledge points:

3.9.5 carry out operations of multiplication and division of two complex numbers expressed in polar form , and corresponding results for division.)

Answer:

Knowledge points:

Solution:

Related Question