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JEE Main & Advanced Mathematics Complex Numbers and Quadratic Equations Question Bank De Moivre's theorem and Roots of unity

  • question_answer
    The value of \[\frac{4(\cos {{75}^{o}}+i\sin {{75}^{o}})}{0.4(\cos {{30}^{o}}+i\sin {{30}^{o}})}\] is

    A) \[\frac{\sqrt{2}}{10}(1+i)\]

    B) \[\frac{\sqrt{2}}{10}(1-i)\]

    C) \[\frac{10}{\sqrt{2}}(1-i)\]

    D) \[\frac{10}{\sqrt{2}}(1+i)\]

    Correct Answer: D

    Solution :

    \[\frac{4(\cos {{75}^{o}}+i\sin {{75}^{o}})}{0.4(\cos {{30}^{o}}+i\sin {{30}^{o}})}\] \[=10(\cos {{75}^{o}}+i\sin {{75}^{o}})(\cos {{30}^{o}}-i\sin {{30}^{o}})\] \[=10(\cos {{45}^{o}}+i\sin {{45}^{o}})=\frac{10}{\sqrt{2}}(1+i)\]


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