What is |g(x)|² for g(x)= 17i - (8+7i)x? A)289 - 238x + 113x² B)289 - 238x - 15x² C)289 + 238x + 113x² D)289 + 238x - 15x² E)-289 + 238x - 113x²

Question

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To find $|g(x)|$, we first need to calculate $g(x) = 17i - (8+7i)x$. Then, to find the magnitude $|g(x)|$, we square the real part and the imaginary part, add them together, and take the square root. However, since the options are given in polynomial form without a square root, we'll just calculate the squared magnitude, which is the sum of the squares of the real and imaginary parts.Given $g(x) = 17i - (8+7i)x$, let's distribute $x$:$$g(x) = 17i - 8x - 7ix$$The real part of $g(x)$ is $-8x$, and the imaginary part is $17 - 7x$.The squared magnitude is:$$|g(x)|^2 = (-8x)^2 + (17 - 7x)^2$$$$= 64x^2 + 289 - 238x + 49x^2$$$$= 113x^2 - 238x + 289$$Since we are looking for the squared magnitude without simplifying it into a square root form, the correct answer is the polynomial that represents this squared magnitude:$$289 - 238x + 113x^2$$This matches option A: $289 - 238x + 113x^2$.

What Is |G(x)|2 for G(x)= 17i - (8+7i)x

What Is |G(x)|² for G(x)= 17i - (8+7i)x