The complex numbers $$\(u\)$$ and $$\(v\)$$ are defined by $$\(u=-4+2 \mathrm{i}\)$$ and $$\(v=3+\mathrm{i}\)$$. Find $$\(\frac{u}{v}\)$$ in the form $$\(x+\mathrm{i} y\)$$, where $$\(x\)$$ and $$\(y\)$$ are real. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

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

Answer:

Multiply numerator and denominator by \(3-\mathrm{i}\)
Obtain numerator \(-10+10 \mathrm{i}\) or denominator 10
Obtain final answer \(-1+\mathrm{i}\)

Knowledge points:

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.)

Solution:

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