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If (x - 3)/(3 + i) + (y - 3)/(3 - i) = i, where x, y are real numbers, then

1. x = 2 and y = -8
2. x = -2 and y = 8
3. x = -2 and y = -6
4. x = 2 and y = 8

Correct answer: x = -2 and y = 8

Solution

Rationalizing gives [(x-3)(3-i) + (y-3)(3+i)]/10 = i; separating real and imaginary parts yields x = -2, y = 8.

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