when does this relation holds?
[z1]-[z2]=[z1+z2] ; [z1] & [z2] represents the modulus of two complex numbers.
to me only when z2=0?
is there any other possibility?
There are other possibilities
$\displaystyle z_1 = \alpha \: e^{i\theta}$ and $\displaystyle z_2 = \beta \: e^{i(\theta+\pi)} = - \beta \: e^{i\theta}$ with $\displaystyle \alpha \geq \beta \geq 0$
Then
$\displaystyle |z_1| = \alpha$ and $\displaystyle |z_2| = \beta$
$\displaystyle z_1 + z_2 = (\alpha - \beta) \: e^{i\theta}$
$\displaystyle |z_1 + z_2| = \alpha - \beta = |z_1| - |z_2|$
For instance
$\displaystyle |2i + (-i)| = |i| = 1 = |2i| - |-i|$