If 4 x+i(3 x-y)=3+i(-6), where x and y are real numbers, then values of x and y.

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4-1.Complex numbers

easy

If $4 x+i(3 x-y)=3+i(-6),$ where $x$ and $y$ are real numbers, then find the values of $x$ and $y.$

A

$x=\frac{3}{4}$,$y=\frac{33}{4}$

B

$x=\frac{3}{4}$,$y=\frac{33}{4}$

C

$x=\frac{3}{4}$,$y=\frac{33}{4}$

D

$x=\frac{3}{4}$,$y=\frac{33}{4}$

Solution

We have

$4 x+i(3 x-y)=3+i(-6)$…..$(1)$

Equating the real and the imaginary parts of $(1)$, we get

$4 x=3,3 x-y=-6$

which, on solving simultaneously, give $x=\frac{3}{4}$ and $y=\frac{33}{4}$

Standard 11

Mathematics

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