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Algebra of Complex Numbers

The real orde...

Question

The real order pair $(x, y)$ which satisfies $(x^{4} + 2 x i) - (3 x^{2} + y i) = (3 - 5 i) + (1 + 2 y i)$ is

(- 2, \frac{1}{3})

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(2, 3)

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(- 2, 3)

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(2, \frac{1}{3})

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Solution

The correct options are
A $(- 2, \frac{1}{3})$
B $(2, 3)$
Given $(x^{4} + 2 x i) - (3 x^{2} + y i) = (3 - 5 i) + (1 + 2 y i)$
$\Rightarrow (x^{4} - 3 x^{2}) + i (2 x - 3 y) = 4 - 5 i$
Equating real and imaginary parts, we get
$x^{4} - 3 x^{2} = 4 \Rightarrow x^{2} = 4 \Rightarrow x = \pm 2$
and $2 x - 3 y = - 5$
$\Rightarrow y = 3, \frac{1}{3}$
Hence $(x, y) \equiv (2, 3), (- 2, \frac{1}{3})$

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