AIEEE 2005 (Offline)Question 1
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 :
Complex Numbers
Solution
Equality in the triangle inequality $|z_1+z_2|\le|z_1|+|z_2|$ holds iff $z_1,z_2$ have the same direction, so $\arg z_1-\arg z_2=0$.