2. Solved Papers
  3. CEE Kerala Engineering

CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2000

  • question_answer
    If\[\theta =\frac{\pi }{6},\]then the 10th term of the series\[1+(\cos \theta +i\sin \theta )+{{(\cos \theta +i\sin \theta )}^{2}}+...\]is:

    A)  \[-1\]                                   

    B)         \[-i\]                    

    C)         \[\frac{1+i\sqrt{3}}{2}\]                              

    D)         \[\frac{1-i\sqrt{3}}{2}\]

    E)         \[-i\]

    Correct Answer: E

    Solution :

    10th term is, \[{{(\cos \theta +i\sin \theta )}^{9}}\] \[\Rightarrow \]               \[\cos 9\theta +i\sin 9\theta \] For        \[\theta =\pi /6\] 10th term \[=\cos \frac{9\pi }{6}+i\sin \frac{9\pi }{6}\]                 \[=\cos \frac{3\pi }{2}+i\sin \frac{3\pi }{2}=-i\]


You need to login to perform this action.
You will be redirected in 3 sec spinner