If $z_1$ and $z_2$ are two complex numbers such that $|z_1+z_2|=|z_1|+|z_2|$, then $\text{arg}(z_1)-\text{arg}(z_2)$ is

Solution

1. The given condition $|z_1+z_2|=|z_1|+|z_2|$ represents the equality case of the triangle inequality for complex numbers.
2. This equality holds if and only if $z_1=k{z}_2$ for some positive real constant $k>0$.
3. Since $z_1$ and $z_2$ are positive scalar multiples of each other, they have the same argument, meaning $\text{arg}(z_1)=\text{arg}(z_2)$.
4. Therefore, the difference $\text{arg}(z_1)-\text{arg}(z_2)=0$.
5. Hence the answer is (A).