Multiple choice

If x = (1 + i) is a root of the equation x2 - x + 1 - i = 0, then the other root is ______________.

  1. 1

  2. -1

  3. 0

  4. None of these
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D Correct answer
Explanation

For a polynomial with real coefficients, complex roots come in conjugate pairs. However, this equation has complex coefficients (1-i). Using the sum of roots = -b/a = 1, if one root is 1+i, the other is 1 - (1+i) = -i.

AI explanation

For a quadratic equation x2 - x + 1 - i = 0 where the coefficients are complex numbers, the sum of the roots does not equal the negative coefficient of x divided by the leading coefficient. Therefore, Vieta's formulas for real coefficients do not apply here. Since no option provides the actual second root of -i, the correct choice is None of these.

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