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JEE Main & Advanced Mathematics Complex Numbers and Quadratic Equations Question Bank Mock Test - Complex Numbers and Quadratic Equations

  • question_answer
    If \[k+\left| k+{{z}^{2}} \right|={{\left| z \right|}^{2}}(k\in {{R}^{-}})\], then possible argument of z is

    A) 0                    

    B)  \[\pi \]       

    C) \[\pi /2\]           

    D) none of these

    Correct Answer: C

    Solution :

    [c] \[\left| k+{{z}^{2}} \right|=\left| {{z}^{2}} \right|-k=\left| {{z}^{2}} \right|+\left| k \right|\] \[\Rightarrow \] \[k,{{z}^{2}}\] and 0+i0 are collinear \[\Rightarrow \] arg (\[{{z}^{2}}\])= arg (k) \[\Rightarrow \] 2 arg (z) = \[\pi \] \[\Rightarrow \] arg (z) = \[\frac{\pi }{2}\]


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