If x = -2 + sqrt{-3},then the value of 2x^4 + | vedclass

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(C) Given $x = -2 + i\sqrt{3}$,we have $x + 2 = i\sqrt{3}$.Squaring both sides,we get $(x + 2)^2 = -3$,which simplifies to $x^2 + 4x + 4 = -3$,or $x^2

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$3$

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(C) Given $x = -2 + i\sqrt{3}$,we have $x + 2 = i\sqrt{3}$.Squaring both sides,we get $(x + 2)^2 = -3$,which simplifies to $x^2 + 4x + 4 = -3$,or $x^2 + 4x + 7 = 0$.Now,we divide the polynomial $P(x) = 2x^4 + 5x^3 + 7x^2 - x + 38$ by $x^2 + 4x + 7$ using polynomial long division:$2x^4 + 5x^3 + 7x^2 - x + 38 = (x^2 + 4x + 7)(2x^2 - 3x + 5) + 3$.Since $x^2 + 4x + 7 = 0$,the expression becomes:$P(x) = 0 	imes (2x^2 - 3x + 5) + 3 = 3$.Thus,the value is $3$.

If $x = -2 + \sqrt{-3}$,then the value of $2x^4 + 5x^3 + 7x^2 - x + 38$ is equal to

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