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JEE Main & Advanced Mathematics Complex Numbers and Quadratic Equations Question Bank Conjugate, Modulus and Argument of complex number

  • question_answer
    If z1, z2 are any two complex numbers, then \[|{{z}_{1}}+\sqrt{z_{1}^{2}-z_{2}^{2}}|\] \[+|{{z}_{1}}-\sqrt{z_{1}^{2}-z_{2}^{2}}|\] is equal to

    A) \[|{{z}_{1}}|\]

    B) \[|{{z}_{2}}|\]

    C) \[|{{z}_{1}}+{{z}_{2}}|\]

    D) \[|{{z}_{1}}+{{z}_{2}}|+|{{z}_{1}}-{{z}_{2}}|\]

    Correct Answer: D

    Solution :

    Trick: Check by putting \[{{z}_{1}}=1+0i\]and \[{{z}_{2}}=0+i\]


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