Constructible number

We say that a nonnegative real number $x$ is constructible if a segment of length $x$ can be constructed with a straight edge and compass starting with a segment of length $1$ .

We say that a complex number $z = x+yi$ is constructible if $|x|$ and $|y|$ are both constructible (we also say that the point $(x,y)$ is constructible). It is easy to show that $x+yi$ is constructible iff the point $(x,y)$ can be constructed with a straight edge and compass in the cartesian plane starting with the points $(0,0)$ and $(1,0)$ .

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Constructible number