A) \[|{{z}_{1}}|+|{{z}_{2}}|\]
B) \[|{{z}_{1}}|-|{{z}_{2}}|\]
C) \[||{{z}_{1}}|-|{{z}_{2}}||\]
D) 0
Correct Answer: C
Solution :
We have \[|{{z}_{1}}-{{z}_{2}}{{|}^{2}}\] \[=|{{z}_{1}}{{|}^{2}}+|{{z}_{2}}{{|}^{2}}-2|{{z}_{1}}||{{z}_{2}}|\cos ({{\theta }_{1}}-{{\theta }_{2}})\] where \[{{\theta }_{1}}=arg({{z}_{1}})\] and \[{{\theta }_{2}}=arg({{z}_{2}})\] Since \[arg\,{{z}_{1}}-arg\,{{z}_{2}}=0\] \\[|{{z}_{1}}-{{z}_{2}}{{|}^{2}}=|{{z}_{1}}{{|}^{2}}+|{{z}_{2}}{{|}^{2}}-2|{{z}_{1}}||{{z}_{2}}|\] \[={{(|{{z}_{1}}|-|{{z}_{2}}|)}^{2}}\] Þ \[|{{z}_{1}}-{{z}_{2}}|=||{{z}_{1}}|-|{{z}_{2}}||\]You need to login to perform this action.
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