The slope of the line $| z 1 | = | z + i |$ is

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Solution

The correct option is D $- 1$
Slope of line $| z - 1 | = | z + 1 |$
$\Rightarrow | (x - 1) + i y | = | x + i (y + 1) |$

$\Rightarrow \sqrt{{(x - 1)}^{2} + y^{2}} = \sqrt{x^{2} + {(y + 1)}^{2}}$
$\Rightarrow x^{2} - 2 x + 1 + y^{2} = x^{2} + y^{2} + 2 y + 1$
$\Rightarrow - 2 x - 2 y = 0$
$\Rightarrow x + y = 0$
$∴ y = - x$
Slope $= - 1.$
Hence, the answer is $- 1.$

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