If $¯ z = 2 - z$ , then locus of $z$ is a

line passing through origin

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line parallel to y-axis

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line parallel to x-axis

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circle

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Solution

The correct option is C line parallel to y-axis
$¯ ¯¯ ¯ Z = 2 - Z \Rightarrow ¯ ¯¯ ¯ Z + Z = 2 Z = x + i y, ¯ ¯¯ ¯ Z = x - i y ∴ ¯ ¯¯ ¯ Z + Z = 2 \Rightarrow x + i y + x - i y = 2 \Rightarrow 2 x = 2 \Rightarrow x = 1$
which is line parallel to y-axis.

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[DSSE 1986]

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