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4-1.Complex numbers
easy
The real values of $x$ and $y$for which the equation is $(x + iy)$ $(2 - 3i)= 4 + i$ is satisfied, are
A
$x = \frac{5}{{13}},y = \frac{8}{{13}}$
B
$x = \frac{8}{{13}},y = \frac{5}{{13}}$
C
$x = \frac{5}{{13}},y = \frac{{14}}{{13}}$
D
None of these
Solution
(c) Equation $(x + iy)(2 – 3i) = 4 + i$
==> $(2x + 3y) + i( – 3x + 2y) = 4 + i$
Equating real and imaginary parts, we get
$2x + 3y = 4$ ……$(i)$
$ – 3x + 2y = 1$……$(ii)$
From $(i)$ and $(ii)$, we get $x = \frac{5}{{13}},y = \frac{{14}}{{13}}$
Aliter : $x + iy = \frac{{4 + i}}{{2 – 3i}} = \frac{{(4 + i)(2 + 3i)}}{{13}} = \frac{5}{{13}} + \frac{{14}}{{13}}i$ .
Std 11
Mathematics
