Values of x and y for which numbers 3 + i{x^2}y and {x^2} + y + 4i are conjugate complex can be

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4-1.Complex numbers

easy

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

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

$( - 1,{\rm{ }}2)$or $( - 2,{\rm{ }}1)$

$(1,\,2)$or $( - 1, - 2)$

None of these

Solution

(a) According to condition, $3 – i{x^2}y = {x^2} + y + 4i$
$⇒$ ${x^2} + y = 3$and ${x^2}y = – 4$ $⇒$ $x = \pm 2,y = – 1$
$⇒$ $(x,y) = (2, – 1)$or $( – 2, – 1)$

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medium

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normal

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

Solution

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For any two complex numbers $z_{1}$ and $z_{2},$ prove that

$\operatorname{Re}\left(z_{1} z_{2}\right)=\operatorname{Re} z_{1} \operatorname{Re} z_{2}-\operatorname{Im} z_{1} \operatorname{Im} z_{2}$