If $z$ is a complex number satisfying $z + ¯ ¯ ¯ z = 0$ , then

I m (z) = 0

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R e (z) = 0

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I m (z) = 1

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R e (z) = 1

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Solution

The correct option is B $R e (z) = 0$
Let $z = x + i y$
$\Rightarrow ¯ z = x - i y$

Given that $z + ¯ z = 0$
$\Rightarrow (x + i y) + (x - i y) = 0 \Rightarrow x = 0 ∴ R e (z) = 0$

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