A) 1
B) \[-1\]
C) 2
D) \[-2\]
Correct Answer: A
Solution :
\[{{\left| 1-{{{\bar{z}}}_{1}}{{z}_{2}} \right|}^{2}}-{{\left| {{z}_{1}}-{{z}_{2}} \right|}^{2}}\] \[=\,\,\,(1-{{\bar{z}}_{1}}{{z}_{2}})\,\,(1-{{z}_{1}}{{\bar{z}}_{2}})-({{z}_{1}}-{{z}_{2}})({{\bar{z}}_{1}}-{{\bar{z}}_{2}})\] \[=\,\,1-{{z}_{1}}{{\bar{z}}_{2}}-\,{{\bar{z}}_{1}}{{z}_{2}}+{{z}_{1}}{{\bar{z}}_{1}}{{z}_{2}}{{\bar{z}}_{2}}-({{z}_{1}}{{\bar{z}}_{1}}-{{z}_{1}}{{\bar{z}}_{2}}-{{\bar{z}}_{1}}{{z}_{2}}+{{z}_{2}}{{\bar{z}}_{2}})\] \[=\,\,1+{{z}_{1}}{{\bar{z}}_{1}}\,{{z}_{2}}{{\bar{z}}_{2}}-{{z}_{1}}{{\bar{z}}_{1}}-{{z}_{2}}{{\bar{z}}_{2}}\] \[=\,\,1+{{\left| {{z}_{1}} \right|}^{2}}{{\left| {{z}_{2}} \right|}^{2}}-{{\left| {{z}_{1}} \right|}^{2}}-{{\left| {{z}_{2}} \right|}^{2}}\] \[=\,\,(1-{{\left| {{z}_{1}} \right|}^{2}})(1-{{\left| {{z}_{2}} \right|}^{2}})\]- \[\Rightarrow \,\,\,\,k=1\]You need to login to perform this action.
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