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

  • question_answer
    If  \[{{z}_{1}}=(4,5)\] and \[{{z}_{2}}=(-3,2)\]then  \[\frac{{{z}_{1}}}{{{z}_{2}}}\] equals [RPET 1996]

    A) \[\left( \frac{-23}{12},\frac{-2}{13} \right)\]

    B)   \[\left( \frac{2}{13},\frac{-23}{13} \right)\]

    C)   \[\left( \frac{-2}{13},\frac{-23}{13} \right)\]

    D) \[\left( \frac{-2}{13},\frac{23}{13} \right)\]

    Correct Answer: C

    Solution :

    \[\frac{{{z}_{1}}}{{{z}_{2}}}=\frac{4+5i}{-3+2i}\times \frac{-3-2i}{-3-2i}\]\[=\frac{-12-8i-15i+10}{9-{{(2i)}^{2}}}\] \[\frac{{{z}_{1}}}{{{z}_{2}}}=\frac{-2}{13}-i\left( \frac{23}{13} \right)=\left( \frac{-2}{13},\frac{-23}{13} \right)\]

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