If $z_1$ and $z_2$ are two non-zero complex numbers such that…

If $z_1$ and $z_2$ are two non-zero complex numbers such that $\left|z_1+z_2\right|=\left|z_1\right|+\left|z_2\right|$ then $\arg z_1-\arg z_2$ is equal to
  1. $\frac{\pi}{2}$
  2. $-\pi$
  3. 0
  4. $-\frac{\pi}{2}$

Solution

$\left|z_1+z_2\right|=\left|z_1\right|+\left|z_2\right| \Rightarrow z_1$ and $z_2$ are collinear and are to the same side of origin; hence $\arg z_1-\arg z_2=0$.

Asked in: JEE Main 2005

Practice more Complex Number questions on Aicharya