If $∣ ∣ z + ¯ ¯ ¯ z ∣ ∣ + ∣ ∣ z - ¯ ¯ ¯ z ∣ ∣ = 2$ , then z lies on

A straight line

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A square

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A circle

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Parabola

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Solution

The correct option is A A straight line
Let $z = x + i y, ¯ z = x - i y$
$z + ¯ z = 2 x, z - ¯ z = 2 i y$
$| z + ¯ z | + | z - ¯ z | = 2 x + 2 y = 2$
$x + y = 2$
Therefore $z$ lies on a straight line.

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