How to decompose a complex number into a sum of two unitary modulus complex numbers? Is it possible to decompose any complex number $z = x + iy\in \mathbb{C}$ with $0\leq|z|\leq2$ into a sum of two unitary modulus exponentials ? i.e. $ z = e^{i\phi_1} + e^{i\phi_2}$ ?
I tried to decompose the problem $x + iy = \cos(\phi_1) + \cos(\phi_2) + i(\sin(\phi_1) + \sin(\phi_2)) $ into a set of two real equations but is seems that they are not linear  :
\begin{eqnarray}
\cos(\phi_1) + \cos(\phi_2) & = &x \\
\sin(\phi_1) + \sin(\phi_2) & = & y
\end{eqnarray}
If it is possible, are there any known algorithm ? I tried the usual trigonometric transformations without success. And formulating the problem in terms of modulus and phase rather than real and imaginary parts made it seem more complex.
Thanks in advance.

Geometrically, it is perfectly possible: in the Argand-Cauchy plane, consider the image $M$ of $z$: $0\le OM=r\le 2$, and the intersections 
$I$ and $J$ of the circle of radius $OM$, centred at $M$. Elementary geometry shows that intersection points exist because$M$ is at distance $ \le 1$ from the unit circle, the quadrilateral $OIMJ$ is a rhombus and
$$\overrightarrow{OM}=\overrightarrow{OI}+\overrightarrow{OJ}.$$
If $z_I, z_J$ are the affixes of these points, this vector relation translates as $\;z=z_I+z_J$.
