If $z_1$ and $z_2$ are two non-zero complex numbers such that $|z_1+z_2|=|z_1|+|z_2|$, then $\arg(z_1)-\arg(z_2)$ is equal to
Step-by-Step Solution
Key Concept: Triangle inequality equality $|z_1+z_2|=|z_1|+|z_2|$ iff $z_1/z_2$ is a positive real number, which is equivalent to $\arg(z_1)=\arg(z_2)$.
**Step 1: State the equality condition**
$|z_1+z_2|=|z_1|+|z_2|$ holds iff $z_1$ and $z_2$ are non-negative real multiples of each other, i.e., $z_1=\lambda z_2$ for some $\lambda>0$.
**Step 2: Conclude on arguments**
$\lambda>0 \Rightarrow \arg(z_1)=\arg(\lambda z_2)=\arg(z_2)$, so $\arg(z_1)-\arg(z_2)=0$.
Correct Answer: 3