A) \[2\left( \left| {{z}_{1}}-{{z}_{2}} \right| \right)\]
B) \[2\left( {{\left| {{z}_{1}} \right|}^{2}}+{{\left| {{z}_{2}} \right|}^{2}} \right)\]
C) \[\left| {{z}_{1}} \right|\left| {{z}_{2}} \right|\]
D) \[{{\left| {{z}_{1}} \right|}^{2}}+{{\left| {{z}_{2}} \right|}^{2}}\]
Correct Answer: B
Solution :
\[{{\left| {{z}_{1}}+{{z}_{2}} \right|}^{2}}+{{\left| {{z}_{1}}-{{z}_{2}} \right|}^{2}}\] \[={{\left| {{z}_{1}} \right|}^{2}}+{{\left| {{z}_{2}} \right|}^{2}}+2\left| {{z}_{1}} \right|\left| {{z}_{2}} \right|+{{\left| {{z}_{1}} \right|}^{2}}+{{\left| {{z}_{2}} \right|}^{2}}-2\left| {{z}_{1}} \right|\left| {{z}_{2}} \right|\] \[=2{{\left| {{z}_{1}} \right|}^{2}}+2{{\left| {{z}_{2}} \right|}^{2}}=2\left[ {{\left| {{z}_{1}} \right|}^{2}}+{{\left| {{z}_{2}} \right|}^{2}} \right]\]
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