• # question_answer Let ${{z}_{1}}$ and ${{z}_{2}}$ be complex number such that$|{{z}_{1}}+{{z}_{2}}|\,\,=\,\,|{{z}_{1}}|+|{{z}_{2}}|$ Statement-1:$\arg \left( \frac{{{z}_{1}}}{{{z}_{2}}} \right)=0$ Statement-2: ${{z}_{1}},\,\,{{z}_{2}}$and origin are collinear and ${{z}_{1}},\,\,{{z}_{2}}$ are on the same side of origin. A)  Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.B)  Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.C)  Statement-1 is true, Statement-2 is false.D)  Statement-1 is false, Statement-2 is true.

$\arg ({{z}_{1}})=\arg ({{z}_{2}})$ $\therefore$$\arg \left( \frac{{{z}_{1}}}{{{z}_{2}}} \right)=\arg ({{z}_{1}})-\arg ({{z}_{2}})=0$