For what real values of x and y are the complex numbers $x^{2} - 7 x + 9 y$ i and $y^{2} i + 20 i - 12$ equal?

(3, 4), (3, 5),(4, 4), (4, 5)

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(4, 3), (5, 3),(4, 4), (4, 5)

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(3, 4), (3, 5),(4, 4), (5, 4)

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(4, 3), (5, 3),(4, 4), (5, 4)

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Solution

The correct option is A (3, 4), (3, 5),(4, 4), (4, 5)
Comparing real and imaginary parts of the given equation, we get
$x^{2} - 7 x = - 12$
$x^{2} - 7 x + 12 = 0$
$(x - 4) (x - 3) = 0$
$x = 4$ and $x = 3$
Also
$9 y = y^{2} + 20$
$y^{2} - 9 y + 20 = 0$
$(y - 4) (y - 5) = 0$
$y = 4$ and $y = 5$ .
$∴ (3, 4), (3, 5), (4, 4), (4, 5)$

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Similar questions

y = \frac{1}{| x - 1 | - x^{2}}

(1) \frac{2}{7}, \frac{6}{7}

(2) \frac{4}{5}, \frac{2}{3}

(3) - \frac{2}{3}, \frac{4}{5}

(4) \frac{7}{9}, - \frac{5}{9}

(5) \frac{- 3}{4}, \frac{+ 5}{4}

(6) \frac{7}{8}, \frac{- 5}{3}

(7) \frac{5}{7}, \frac{11}{7}

(8) 0, \frac{- 3}{4}

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