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Solve the quadratic equation i*x² - 3x - 2i = 0 over the complex numbers and write each root in the form a + ib with a, b real.

1. x = -i and x = -2i
2. x = i and x = 2i
3. x = -i and x = 2i
4. x = 2 and x = i

Correct answer: x = -i and x = -2i

Solution

Dividing by i gives x² + 3i*x - 2 = 0, which factors as (x + i)(x + 2i) = 0, so the roots are x = -i and x = -2i.

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