The complex numbers $$$u$$$ and $$$v$$$ are defined by $$$u=-4+2 \mathrm{i}$$$ and $$$v=3+\mathrm{i}$$$. In an Argand diagram, with origin $$$O$$$, the points $$$A, B$$$ and $$$C$$$ represent the complex numbers $$$u, v$$$ and $$$2 u+v$$$ respectively. State fully the geometrical relationship between $$$O A$$$ and $$$B C$$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

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

Answer:

State that $O A$ and $B C$ are parallel
State that $B C=2 O A$

Knowledge points:

3.9.1 understand the idea of a complex number, recall the meaning of the terms real part, imaginary part, modulus, argument, conjugate, and use the fact that two complex numbers are equal if and only if both real and imaginary parts are equal

3.9.2 carry out operations of addition, subtraction, multiplication and division of two complex numbers expressed in Cartesian form (For calculations involving multiplication or division, full details of the working should be shown.)

Answer:

Knowledge points:

Solution:

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