A) \[({{a}^{2}}+{{b}^{2}})(|{{z}_{1}}|+|{{z}_{2}}|)\]
B) \[({{a}^{2}}+{{b}^{2}})(|{{z}_{1}}{{|}^{2}}+|{{z}_{2}}{{|}^{2}})\]
C) \[({{a}^{2}}+{{b}^{2}})(|{{z}_{1}}{{|}^{2}}-|{{z}_{2}}{{|}^{2}})\]
D) None of these
Correct Answer: B
Solution :
\[|(a{{z}_{1}}-b{{z}_{2}}){{|}^{2}}+|(b{{z}_{1}}+a{{z}_{2}}){{|}^{2}}\] \[={{a}^{2}}|{{z}_{1}}{{|}^{2}}+{{b}^{2}}|{{z}_{2}}{{|}^{2}}-2\operatorname{Re}(ab)|{{z}_{1}}{{\overline{z}}_{2}}|+{{b}^{2}}|{{z}_{1}}{{|}^{2}}+\] \[{{a}^{2}}|{{z}_{2}}{{|}^{2}}+2\operatorname{Re}(ab)|{{\overline{z}}_{1}}{{z}_{2}}|\] \[=({{a}^{2}}+{{b}^{2}})(|{{z}_{1}}{{|}^{2}}+|{{z}_{2}}{{|}^{2}})\]You need to login to perform this action.
You will be redirected in
3 sec