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JEE Main & Advanced Sample Paper JEE Main Sample Paper-7

  • question_answer
    If \[{{z}_{1}}\] and \[{{z}_{2}}\] are unimodular complex number that satisfy \[z_{1}^{2}+z_{2}^{2}=4\] and then \[\left( {{z}_{1}}+{{\overline{z}}_{1}} \right)+{{\left( {{z}^{2}}+{{\overline{z}}^{2}} \right)}^{2}}\] is equal to

    A)  10                                         

    B)  12

    C)  14                                         

    D)  16

    Correct Answer: B

    Solution :

    \[\because \]  \[z_{1}^{2}+z_{2}^{2}=4\] \[\Rightarrow \,\,\overline{z}_{1}^{2}+\overline{z}_{2}^{2}=4\] \[\therefore \,\,{{({{z}_{1}}+{{z}_{1}})}^{2}}+{{({{z}_{2}}+{{\overline{z}}_{2}})}^{2}}\] \[=z_{1}^{2}+\overline{z}_{1}^{2}+2{{z}_{1}}{{\overline{z}}_{1}}+z_{2}^{2}+\overline{z}_{2}^{2}+2{{z}_{2}}{{\overline{z}}_{2}}\] \[=\left( z_{1}^{2}+z_{2}^{2} \right)+\left( z_{1}^{2}+z_{2}^{2} \right)+4=12\].


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