Set complexity of construction of a regular polygon

Given a subset of $\mathbb{C}$ containing $x,y$, one can add $x + y,,x - y,,xy$or(when$y\ne0$)$x/y$orany$z$suchthat$z^2=x$\mathrm{.}Let$p$ be a prime Fermat number. We prove that it is possible to obtain from $\{1\}$ a set containing all the $p$-th roots of 1 by $12p^2$ above operations. This result is different from the standard estimation of complexity of an algorithm computing the $p$-th roots of 1.