# Question #0f1ea

Calling $z = x + i y$ we have $\left\mid z \right\mid = \sqrt{z \overline{z}} = \sqrt{\left(x + i y\right) \left(x - i y\right)} = \sqrt{{x}^{2} + {y}^{2}}$ so
$\left\mid z \right\mid = 1$ corresponds to a circle centered at the origin of coordinates, with radius 1. Squaring both sides
${x}^{2} + {y}^{2} = 1$