If the conjugate of $(x + i y) (1 - 2 i)$ is $(1 + i)$ , then

x + i y = 1 - i

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x + i y = \frac{1 - i}{1 - 2 i}

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x - i y = \frac{1 - i}{1 + 2 i}

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x - i y = \frac{1 - i}{1 + i}

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Solution

The correct option is B $x + i y = \frac{1 - i}{1 - 2 i}$
$¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ (x + i y) (1 - 2 i) = 1 + i$

Or, $(x + i y) (1 - 2 i) = 1 - i$

Thus, $(x + i y) = \frac{1 - i}{1 - 2 i}$

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