A) \[25,\,\,19\]
B) \[19,\,\,25\]
C) \[-19,\,\,-25\]
D) \[-25,\,\,-19\]
Correct Answer: A
Solution :
\[\left| {{z}_{1}}+{{z}_{2}} \right|\le \left| {{z}_{1}} \right|+\left| {{z}_{2}} \right|=\left| 24+7i \right|+6=25+6=31\] Also, \[\Rightarrow \,\,\,\,\left| {{z}_{1}}+{{z}_{2}} \right|=\,\,\left| {{z}_{1}}-(-{{z}_{2}}) \right|\ge \left| \left| {{z}_{1}} \right|-\left| {{z}_{2}} \right| \right|\] \[\Rightarrow \,\,\,\,\left| {{z}_{1}}+{{z}_{2}} \right|\,\,\ge \,\,\left| 25-6 \right|=19\] Hence the least value of \[\left| {{z}_{1}}+{{z}_{2}} \right|\] is 19 and the greatest value is 25.
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