Question

find x and y if 2x+4iy= -i^3 x-y+3

Answer 1

$\underline{\textsf{Given:}}$

$\mathsf{2x+i\,4y=-i^3x-y+3}$

$\underline{\textsf{To find:}}$

$\textsf{The value of x and y}$

$\underline{\textsf{Solution:}}$

$\textsf{Consider,}$

$\mathsf{2x+i\,4y=-i^3x-y+3}$

$\mathsf{2x+i\,4y=-(-i)x-y+3}$

$\mathsf{2x+i\,4y=i\,x-y+3}$

$\mathsf{2x+i\,4y=(-y+3)+i\,x}$

$\textsf{Separating real and imaginary parts on bothsides, we get}$

$\mathsf{2x=-y+3}\;\;\textsf{and}\;\;\mathsf{x=4y}$

$\implies\mathsf{2(4y)=-y+3}$

$\implies\mathsf{8y=-y+3}$

$\implies\mathsf{9y=3}$

$\implies\mathsf{y=\dfrac{3}{9}}$

$\implies\mathsf{y=\dfrac{1}{3}}$

$\textsf{when}\;\mathsf{y=\dfrac{1}{3}}$

$\mathsf{x=4(\dfrac{1}{3})=\dfrac{4}{3}}$

$\underline{\textsf{Answer:}}$

$\mathsf{x=\dfrac{4}{3}\;\;\&\;\;y=\dfrac{1}{3}}$

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