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

  • question_answer
     \[arg\left( \frac{3+i}{2-i}+\frac{3-i}{2+i} \right)\] is equal to

    A) \[\frac{\pi }{2}\]

    B) \[-\frac{\pi }{2}\]

    C) 0

    D) \[\frac{\pi }{4}\]

    Correct Answer: C

    Solution :

    \[arg\left( \frac{3+i}{2-i}+\frac{3-i}{2+i} \right)=arg\left( \frac{6+5i+{{i}^{2}}+6-5i+{{i}^{2}}}{5} \right)\] \[=arg\left( \frac{10}{5} \right)=0\].


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