11th Class Mathematics Sample Paper Mathematics Olympiad - Sample Paper-4

  • question_answer Multiplicative inverse of \[\frac{3+4i}{4-4i}\]is

    A) \[\frac{8}{25}-\frac{31}{25}i\]               

    B) \[\frac{-8}{25}-\frac{31}{25}i\]       

    C) \[\frac{-8}{25}+\frac{31}{25}i\]            

    D) None of these

    Correct Answer: D

    Solution :

    [d] \[z=\frac{3+4i}{4-4i}=\frac{\left( 3+4i \right)\left( 4+4i \right)}{\left( 4-4i \right)\left( 4+4i \right)}=\frac{-4+28i}{16+16}=\frac{-1+7i}{8}\] Multiplicative inverse of \[z=\frac{1}{z}=\frac{8}{-1+7i}=\frac{8(-1-7i)}{{{(-1)}^{2}}-{{(-7i)}^{2}}}=\frac{8(1+7i)}{50}=-\frac{4(1+7i)}{25}=\frac{-4}{25}-\frac{28}{25}i\] Hence, option [d] is correct.

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