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.

No. it is not, because$$\left|e^{i\phi_1}+e^{i\phi_2}\right|\leqslant1+1=2.$$
