A) \[|{{z}_{1}}-{{z}_{2}}{{|}^{2}}\]
B) \[-|{{z}_{1}}-{{z}_{2}}{{|}^{2}}\]
C) \[|{{z}_{1}}{{|}^{2}}+|{{z}_{2}}{{|}^{2}}\]
D) \[|{{z}_{1}}{{|}^{2}}-|{{z}_{2}}{{|}^{2}}\]
E) \[|{{z}_{1}}{{|}^{2}}+|{{z}_{2}}{{|}^{2}}-2|{{z}_{1}}||{{z}_{2}}|\]
Correct Answer: B
Solution :
Given, \[{{z}_{1}}=3+4i,{{z}_{2}}=-1+2i\] then, \[|{{z}_{1}}+{{z}_{2}}{{|}^{2}}-2(|{{z}_{1}}{{|}^{2}}+|{{z}_{2}}{{|}^{2}}=?\] We know that, by parallelogram law, \[|{{z}_{1}}+{{z}_{2}}{{|}^{2}}+|{{z}_{1}}-{{z}_{2}}{{|}^{2}}=2(|{{z}_{1}}{{|}^{2}}+|{{z}_{2}}{{|}^{2}})\] \[\Rightarrow \]\[|{{z}_{1}}+{{z}_{2}}{{|}^{2}}-2(|{{z}_{1}}{{|}^{2}}+|{{z}_{2}}{{|}^{2}})=-|{{z}_{1}}-{{z}_{2}}{{|}^{2}}\] Here,\[LHS=-20\]and\[RHS=-20\]You need to login to perform this action.
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