If $a + i b$ is a root of the equation $x^{2} - a x + b$ , then (where $i = \sqrt{- 1}$ )

b = 1

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b = - 1

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b = \pm 1

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none of these

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Solution

The correct option is A $b = 1$
$a + ι b$ is one root then $a - ι b$ is another root

$a = a + ι b + a - ι b$

$2 a = a \Rightarrow a = 0$

$(a + ι b) (a - ι b) = b$

$a^{2} + b^{2} = b$

$b = 0, 1$

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