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  3. CEE Kerala Engineering

CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2003

  • question_answer
    The value of \[\left( \cos \frac{\pi }{2}+i\sin \frac{\pi }{2} \right)\left[ \cos \left( \frac{\pi }{{{2}^{2}}} \right)+i\sin \left( \frac{\pi }{{{2}^{2}}} \right) \right]\] \[\left[ \cos \left( \frac{\pi }{{{2}^{3}}} \right)+i\sin \left( \frac{\pi }{{{2}^{3}}} \right) \right].....\infty \]is:

    A)  \[-1\]                                   

    B)  \[1\]                    

    C)  \[0\]                    

    D)         \[\sqrt{2}\]

    E)  \[-\sqrt{2}\]

    Correct Answer: A

    Solution :

    \[\left( \cos \frac{\pi }{2}+i\sin \frac{\pi }{2} \right)\left( \cos \frac{\pi }{{{2}^{2}}}+i\sin \frac{\pi }{{{2}^{2}}} \right)....\infty \] \[=\cos \left( \frac{\pi }{2}+\frac{\pi }{{{2}^{2}}}+....\infty  \right)+i\sin \left( \frac{\pi }{2}+\frac{\pi }{{{2}^{2}}}+....\infty  \right)\] \[=\cos \left( \frac{\pi }{2}.\frac{1}{1-\frac{1}{2}} \right)+i\sin \left( \frac{\pi }{2}.\frac{1}{1-\frac{1}{2}} \right)\] \[=\cos \pi +i\sin \pi \] \[=-1\]


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