A) \[{{m}_{1}}<{{m}_{2}}<{{m}_{3}}<{{m}_{4}}\]
B) \[{{m}_{4}}<{{m}_{3}}<{{m}_{2}}<{{m}_{1}}\]
C) \[{{m}_{3}}<{{m}_{2}}<{{m}_{4}}<{{m}_{1}}\]
D) \[{{m}_{3}}<{{m}_{1}}<{{m}_{2}}<{{m}_{4}}\]
Correct Answer: C
Solution :
Let \[{{z}_{1}}=1+4i,\,\,{{z}_{2}}=3+i,\,\,{{z}_{3}}=1-i\,\,and\,{{z}_{4}}=2-3\,i\] \[\therefore \,\,\,{{m}_{1}}=\,\left| {{z}_{1}} \right|,\,\,{{m}_{2}}=\,\left| {{z}_{2}} \right|,\,{{m}_{3}}=\,\,\,\left| {{z}_{3}} \right|\,\,and\,\,{{m}_{4}}=\,\left| {{z}_{4}} \right|\] \[\Rightarrow \,\,\,{{\operatorname{m}}_{1}}=\,\,\sqrt{17},\,\,\,{{m}_{2}}=\,\sqrt{10},\,\,{{m}_{3}}=\sqrt{2},\,\,and\,\,{{m}_{4}}=\sqrt{13},\] \[\Rightarrow \,\,\,{{\operatorname{m}}_{3}}<{{m}_{2}}<{{m}_{4}}<{{m}_{1}}.\]
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