| 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.
Correct Answer: A
Solution :
\[\arg ({{z}_{1}})=\arg ({{z}_{2}})\] \[\therefore \]\[\arg \left( \frac{{{z}_{1}}}{{{z}_{2}}} \right)=\arg ({{z}_{1}})-\arg ({{z}_{2}})=0\]
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