Multiple choice

If one root of the equation $x ^ { 2 } + ( 1 - 3 i ) x - 2 ( 1 + i ) = 0$ is $- 1 + i,$ then the other root is

  1. $- 1 - i$
  2. $\dfrac { - 1 - i } { 2 }$
  3. $i$
  4. $2i$
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D Correct answer
Explanation

For a quadratic equation with complex coefficients, the sum of roots is -b/a = -(1-3i) = -1+3i. Let the roots be r1 and r2. r1 = -1+i. r1+r2 = -1+3i. (-1+i) + r2 = -1+3i. r2 = 2i.

AI explanation

In a quadratic equation, the sum of the roots is equal to the negation of the coefficient of x. For the equation x^2 + (1 - 3i)x - 2(1 + i) = 0, the sum of the roots is -1 + 3i. Given that one root is -1 + i, we subtract this from the total sum to find the other root. Calculating (-1 + 3i) - (-1 + i) gives 2i, which is the other root.

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