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Complex Numbers

If 2 - i×a ...

Question

If $(2 - i) \times (a - b i) = 2 + 9 i$ , where i is the imaginary unit and a and b are real numbers, then a equals

A

3

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B

2

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C

1

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D

0

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E

- 1

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Solution

The correct option is B $- 1$
Given, $(2 - i) (a - b i) = 2 a - 2 b i - a i - b$
$= (2 a - b) + i (- a - 2 b)$
$= 2 + 9 i$
By comparing, we get $2 a - b = 2$ and $a + 2 b = - 9$
By solving, we get $a = - 1$ and $b = - 4$

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