Multiple choice

One root of the equation $\displaystyle x^{2} - ix - \left ( 1 + i \right )=0$ is $\displaystyle 1 + i$, where $i=\sqrt{-1}$, then other root is

  1. $\displaystyle 1 - i$
  2. $\displaystyle -1 - i$
  3. $\displaystyle -1 + i$
  4. $\displaystyle -1$
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D Correct answer
Explanation

For a quadratic equation with complex coefficients, the roots do not necessarily come in conjugate pairs. Using the sum of roots: (1+i) + r2 = -(-i) = i. Therefore, r2 = i - (1+i) = -1.

AI explanation

By Vieta's formulas for the equation x squared - ix - (1 + i) = 0, the sum of the roots equals i. Given that one root is 1 + i, let the other root be r, so (1 + i) + r = i. Solving this gives r = -1.

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