If $(5 + 3 i) (x + i y) = 3 - 4 i$ then $34 x =$

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Solution

The correct option is B $3$
$(5 + 3 i) (x + i y) = 3 - 4 i$
L.H.S. $= (5 x - 3 y) + (5 y + 3 x) i = 3 - 4 i$
$5 x - 3 y = 3$
$5 y + 3 x = - 4$
Solving the equations simultaneously,
$x = \frac{3}{34}; y = \frac{- 29}{34}$
$∴ 34 x = 34 \times \frac{3}{34}$
$= 3$

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