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4-1.Complex numbers
medium
If $x,y \in R$and $(x + iy)(3 + 2i) = 1 + i$, then $(x,\,y)$ is
A
$\left( {1,\frac{1}{5}} \right)$
B
$\left( {\frac{1}{{13}},\frac{1}{{13}}} \right)$
C
$\left( {\frac{5}{{13}},\frac{1}{{13}}} \right)$
D
$\left( {\frac{1}{5},\frac{1}{5}} \right)$
Solution
(c) $x + iy = \left( {\frac{{1 + i}}{{3 + 2i}}} \right)\frac{{(3 – 2i)}}{{(3 – 2i)}} = \frac{{5 + i}}{{13}}$
Hence $x = \frac{5}{{13}},y = \frac{1}{{13}}$.
Standard 11
Mathematics
