The complex numbers $$\(u\)$$ and $$\(v\)$$ are defined by $$\(u=-4+2 \mathrm{i}\)$$ and $$\(v=3+\mathrm{i}\)$$. Hence express $$\(\frac{u}{v}\)$$ in the form $$\(r \mathrm{e}^{\mathrm{i} \theta}\)$$, where $$\(r\)$$ and $$\(\theta\)$$ are exact. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics
IGCSE&ALevel
CAIE
Exam No:9709_m21_qp_32 Year:2021 Question No:8(b)

Answer:

State or imply \(r=\sqrt{2}\)
State or imply that \(\theta=\frac{3}{4} \pi\)

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

Solution:

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