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Value of a polynomial at a given complex number x (use the quadratic x satisfies)

This type of question, asked 3 times: 11 May 2024 S2, 23 Apr 2025 S1, 14 May 2026 S1. All 3 questions below, oldest first.

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  1. Question 1

    11 May 2024 S2

    116
    If x=51−2ix = \frac{5}{1-2i}, i=−1i=\sqrt{-1}, then the value of x3+x2−x+22x^3+x^2-x+22 is

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  2. Question 2

    23 Apr 2025 S1

    146
    If x=−2+−3x= - 2 +\sqrt{- 3}, then the value of 2x4+5x3+7x2−x+382x^{4}+ 5x^{3}+ 7x^{2}-x+ 38 is equal to

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  3. Question 3

    14 May 2026 S1

    55
    If x=253−4ix = \dfrac{25}{3 - 4i} then 2x3−11x2+44x+27=2x^3 - 11x^2 + 44x + 27 =

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