A) 0
B) 2
C) 7
D) 17
Correct Answer: B
Solution :
(b)\[\therefore \left| {{z}_{1}}-{{z}_{2}}\left| \,\ge \, \right|\,\left| {{z}_{1}} \right|-\left| {{z}_{2}} \right| \right|\] |
\[\therefore \left| {{z}_{2}}-3-4i\left| \,\ge \, \right. \right|\left| {{z}_{2}} \right|\left. - \right|\left. \left. 3+4i \right| \right|\] |
\[\Rightarrow 5\ge \left| \left| {{z}_{2}} \right|-54 \right|\] \[\Rightarrow -5\le \left| {{z}_{2}} \right|-5\le 5\Rightarrow \left| {{z}_{2}} \right|\le 10\] \[\Rightarrow -\left| {{z}_{2}} \right|\ge -10\] |
\[\therefore \left| {{z}_{1}} \right|-\left| {{z}_{2}} \right|\ge 12-10=2\] |
But\[\left| {{z}_{1}}-{{z}_{2}} \right|\ge \left| {{z}_{1}} \right|-\left| {{z}_{2}} \right|\ge 2\] \[\Rightarrow \]Minimum value of \[\left| {{z}_{1}}-{{z}_{2}} \right|\,\,\operatorname{is}\,\,2.\]. |
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