The real values of x and y for which the equa | vedclass

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(C) Given equation: $({x^4} + 2xi) - (3{x^2} + yi) = (3 - 5i) + (1 + 2yi)$Rearranging the terms,we get: $({x^4} - 3{x^2}) + i(2x - y) = 4 + i(2y - 5)$

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Both $(a)$ and $(b)$

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(C) Given equation: $({x^4} + 2xi) - (3{x^2} + yi) = (3 - 5i) + (1 + 2yi)$Rearranging the terms,we get: $({x^4} - 3{x^2}) + i(2x - y) = 4 + i(2y - 5)$Equating real and imaginary parts:Real part: ${x^4} - 3{x^2} = 4 \Rightarrow {x^4} - 3{x^2} - 4 = 0$Let ${x^2} = t$,then $t^2 - 3t - 4 = 0 \Rightarrow (t - 4)(t + 1) = 0$Since $x$ is real,$x^2 = 4 \Rightarrow x = \pm 2$Imaginary part: $2x - y = 2y - 5 \Rightarrow 2x + 5 = 3y$Case $1$: If $x = 2$,then $2(2) + 5 = 3y$ $\Rightarrow 9 = 3y$ $\Rightarrow y = 3$Case $2$: If $x = -2$,then $2(-2) + 5 = 3y$ $\Rightarrow 1 = 3y$ $\Rightarrow y = \frac{1}{3}$Thus,both pairs $(2, 3)$ and $(-2, \frac{1}{3})$ satisfy the equation.

The real values of $x$ and $y$ for which the equation $({x^4} + 2xi) - (3{x^2} + yi) = (3 - 5i) + (1 + 2yi)$ is satisfied,are

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