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

ধরি,

$\begin{array}{l} z_{1}=\cos \theta_{1}+i \sin \theta_{1}, \quad z_{2}=\cos \theta_{2}+i \sin \theta_{2} \\ z_{1}+z_{2}=\left(\cos \theta_{1}+\cos \theta_{2}\right)+i\left(\sin \theta_{1}+\sin \theta_{2}\right) \\ \left|z_{1}+z_{2}\right|=\left|z_{1}\right|+\left|z_{2}\right| \\ \text { বা, } \sqrt{\left(\cos \theta_{1}+\cos \theta_{2}\right)^{2}+\left(\sin \theta_{1}+\sin \theta_{2}\right)^{2}}=1+1 \\ বা,~ 2\left(1+\cos \left(\theta_{1}-\theta_{2}\right)\right)=4 \\ \therefore \theta_{1}-\theta_{2}=0 \\ \therefore \arg z_{1}-\arg z_{2}=0 \end{array}$