JEE Main & Advanced Mathematics Complex Numbers and Quadratic Equations Question Bank Integral power of iota, Algebraic operations and Equality of complex numbers

  • question_answer \[\frac{\sqrt{5+12i}+\sqrt{5-12i}}{\sqrt{5+12i}-\sqrt{5-12i}}=\]

    A) \[-\frac{3}{2}i\]

    B) \[\frac{3}{2}i\]

    C) \[-\frac{3}{2}\]

    D) \[\frac{3}{2}\]

    Correct Answer: A

    Solution :

    \[\frac{(\sqrt{5+12i}+\sqrt{5-12i})(\sqrt{5+12i}+\sqrt{5-12i})}{(\sqrt{5+12i}-\sqrt{5-12i})(\sqrt{5+12i}+\sqrt{5-12i})}\] \[=\frac{5+12i+5-12i+2\sqrt{5+12i}\sqrt{5-12i}}{5+12i-5+12i}\] \[=\frac{10+2\times (\pm 13)}{24i}=-\frac{3}{2}i\]or \[\frac{2i}{3}\].


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