Page 2 of 2 FirstFirst 12
Results 16 to 23 of 23

Math Help - Find the value of Z^69

  1. #16
    Super Member malaygoel's Avatar
    Joined
    May 2006
    From
    India
    Posts
    648
    Quote Originally Posted by zorro View Post
    It is
    \frac{\sqrt{3}+i}{2}
    Now please can any one give me the right solution to this question?
    The solution has been given above...see the first two replies of this thread.
    Follow Math Help Forum on Facebook and Google+

  2. #17
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,835
    Thanks
    1604
    Quote Originally Posted by zorro View Post
    It is
    \frac{\sqrt{3}+i}{2}
    Now please can any one give me the right solution to this question?
    z = \frac{\sqrt{3}}{2} + \frac{1}{2}i.

    Changing to polars gives:

    |z| = \sqrt{\left(\frac{\sqrt{3}}{2}\right)^2 + \left(\frac{1}{2}\right)^2}

     = \sqrt{\frac{3}{4} + \frac{1}{4}}

     = \sqrt{1}

     = 1



    \theta = \arctan{\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}}

     = \arctan{\frac{1}{\sqrt{3}}}

     = \frac{\pi}{6}.


    So z = \frac{\sqrt{3}}{2} + \frac{1}{2}i = 1\,\textrm{cis}\,{\frac{\pi}{6}}.


    Now, using DeMoivre's Theorem...


    z^{69} = 1^{69}\,\textrm{cis}\,{\frac{69\pi}{6}}

     = \textrm{cis}\,{\frac{3\pi}{2}}

     = \cos{\frac{3\pi}{2}} + i\sin{\frac{3\pi}{2}}

    =-i.
    Follow Math Help Forum on Facebook and Google+

  3. #18
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by zorro View Post
    It is
    \frac{\sqrt{3}+i}{2}
    Now please can any one give me the right solution to this question?
    See Soroban's post.

    We are more interested in you acquiring a fishing net than giving you this fish.

    CB
    Follow Math Help Forum on Facebook and Google+

  4. #19
    Banned
    Joined
    Dec 2008
    From
    Mauritius
    Posts
    523
    Quote Originally Posted by mr fantastic View Post
    There is no simple exact answer to the question you have posted. This has been said several times now.

    So either the question has a mistake in it or an approximate answer is required. If the former, then the likely question and its answer has been given in this thread. If the latter, the answer has also been given.

    I don't see how any further progress can be made here unless the OP is prepared to acknowledge and address the above issues.


    Sorry fr the mistake the question is:

    If  z = \frac{\sqrt{3}+i}{2} ; find the value z^{69}
    Follow Math Help Forum on Facebook and Google+

  5. #20
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,835
    Thanks
    1604
    Quote Originally Posted by zorro View Post
    Sorry fr the mistake the question is:

    If  z = \frac{\sqrt{3}+i}{2} ; find the value z^{69}

    Take the time to read the responses you've gotten. Two people have told you a method of how to solve it, and I've posted the solution for you.
    Follow Math Help Forum on Facebook and Google+

  6. #21
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by zorro View Post
    It is
    \frac{\sqrt{3}+i}{2}
    Now please can any one give me the right solution to this question?
    Posts #2 and #3 tell you what to do. What part of their instruction don't you understand?
    Follow Math Help Forum on Facebook and Google+

  7. #22
    Banned
    Joined
    Dec 2008
    From
    Mauritius
    Posts
    523

    I didnt get the middle portion

    Quote Originally Posted by mr fantastic View Post
    Posts #2 and #3 tell you what to do. What part of their instruction don't you understand?

    How is cos(69. \frac{\pi}{6}) + i sin(69. \frac{ \pi}{6}) = cos \frac{3 \pi}{2} + i sin \frac{3 \pi}{2}

    could u please explain
    Follow Math Help Forum on Facebook and Google+

  8. #23
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,835
    Thanks
    1604
    \frac{69\pi}{6} = \frac{23\pi}{2}.

    This angle is the same as \frac{3\pi}{2}, just having gone around the unit circle five times.
    Last edited by Prove It; December 14th 2009 at 03:31 PM.
    Follow Math Help Forum on Facebook and Google+

Page 2 of 2 FirstFirst 12

Similar Math Help Forum Discussions

  1. Replies: 8
    Last Post: March 22nd 2011, 05:57 PM
  2. Replies: 2
    Last Post: July 5th 2010, 09:48 PM
  3. Replies: 1
    Last Post: February 17th 2010, 04:58 PM
  4. Replies: 0
    Last Post: June 16th 2009, 01:43 PM
  5. Replies: 2
    Last Post: April 6th 2009, 09:57 PM

Search Tags


/mathhelpforum @mathhelpforum