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Find all real numbers x and y for which the complex numbers (-3 + i*x²*y) and (x² + y + 4i) are conjugates of each other.

1. x = 1, y = -4 or x = -1, y = -4
2. x = 2, y = -7 or x = -2, y = -7
3. x = 1, y = 4 only
4. x = 0, y = -3 only

Correct answer: x = 1, y = -4 or x = -1, y = -4

Solution

Equating real parts and opposite imaginary parts gives x² + y = -3 and x²*y = -4, whose real solution is x = ±1, y = -4.

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