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Conjugate of a Complex Number

The values of...

Question

The values of x and y for which the numbers 3+i $x^{2}$ y and $x^{2}$ +y+4i are conjugate complex are

(-2,-1) or (2,-1)

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(1,-2) or (-2,1)

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(1,2) or (-1,-2)

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None of these

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Solution

The correct option is A
(-2,-1) or (2,-1)

According to condition, 3-i $x^{2}$ y = $x^{2}$ + y + 4i

⇒ $x^{2}$ + y = 3 And $x^{2}$ y = -4 ⇒ x = ±2, y = -1

⇒ (x,y) = (2,-1) or (-2,-1)

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