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Easy

Question

If z=x+ i y is a variable complex number such that arg⁡( $open parentheses fraction numerator straight z minus 1 over denominator straight z plus 1 end fraction close parentheses equals straight pi over 4$ then

$x^{2} - y^{2} - 2 x = 1$
$x^{2} + y^{2} - 2 x = 1$
$x^{2} + y^{2} - 2 y = 1$
$x^{2} + y^{2} + 2 y = 1$

The correct answer is: $straight x squared plus straight y squared minus 2 straight x equals 1$

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