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 \[x=3+i\],  then \[{{x}^{3}}-3{{x}^{2}}-8x+15=\] [UPSEAT 2003]

    A) 6

    B) 10

    C) - 18

    D) - 15

    Correct Answer: D

    Solution :

    \[x=3+i\,\Rightarrow \,\,x-3=i\,\] \[\Rightarrow \]  \[\,{{x}^{2}}-6x+10=0\]  Þ  \[{{x}^{3}}-3{{x}^{2}}-8x+15\]  \[=x({{x}^{2}}-6x+10)+3\,({{x}^{2}}-6x+10)-15\] \[=x(0)+3(0)-15=-15\].

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