Proposition 6.4.13.label Let $A$ be a unital $C^{*}$-algebra then every element $x\in A$ is a linear combination of four unitary elements.
Proof. Let $h\in A_{h}$ with $\norm{h}{}\leq 1$ and set $u=h+i(1-h^{2})^{1/2}$. By Proposition 6.4.8, $u$ is unitary and $h=\frac{1}{2}(u+u^{*})$. For general $x\in A$ we consider the real and imaginary parts of $x/\norm{x}{}$$\square$