Results 1 to 4 of 4

Math Help - De Moivre's Theorem of Complex numbers Question Help

  1. #1
    Newbie
    Joined
    May 2012
    From
    Delhi
    Posts
    3

    Post De Moivre's Theorem of Complex numbers Question Help

    Hi I'm having trouble solving this complex number problem. If anyone can help me out i will really appreciate it. Thanks

    here is the question
    Use De Moivre's Theorem to solve this equation z9 + z5 - z4 -1 = 0?

    I just want to know how can i start solving this??
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jun 2009
    Posts
    658
    Thanks
    131

    Re: De Moivre's Theorem of Complex numbers Question Help

    The LHS will factorise. Then you can equate each factor to zero.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,318
    Thanks
    1234

    Re: De Moivre's Theorem of Complex numbers Question Help

    Quote Originally Posted by BobP View Post
    The LHS will factorise. Then you can equate each factor to zero.
    And it factorises to...

    \displaystyle \begin{align*} z^9 + z^5 - z^4 - 1 &\equiv z^9 - z^4 + z^5 - 1 \\ &\equiv z^4\left(z^5 - 1\right) + 1\left(z^5 - 1\right) \\ &\equiv \left(z^5 - 1\right)\left(z^4 + 1\right) \end{align*}

    So that means you can set \displaystyle \begin{align*} z^5 - 1 = 0 \end{align*} and \displaystyle \begin{align*} z^4 + 1 = 0 \end{align*} and solve using DeMoivre's Theorem
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    May 2012
    From
    Delhi
    Posts
    3

    Re: De Moivre's Theorem of Complex numbers Question Help

    Quote Originally Posted by Prove It View Post
    And it factorises to...

    \displaystyle \begin{align*} z^9 + z^5 - z^4 - 1 &\equiv z^9 - z^4 + z^5 - 1 \\ &\equiv z^4\left(z^5 - 1\right) + 1\left(z^5 - 1\right) \\ &\equiv \left(z^5 - 1\right)\left(z^4 + 1\right) \end{align*}

    So that means you can set \displaystyle \begin{align*} z^5 - 1 = 0 \end{align*} and \displaystyle \begin{align*} z^4 + 1 = 0 \end{align*} and solve using DeMoivre's Theorem
    Thanks alot!
    i am able to solve it now, it was pretty simple. thanks again
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. de Moivre's Theorem
    Posted in the Pre-Calculus Forum
    Replies: 7
    Last Post: May 8th 2011, 03:28 AM
  2. De Moivre's Theorem and Nth Roots of Unity Question
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: April 17th 2011, 11:58 AM
  3. complex numbers- hurwitz theorem
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: November 23rd 2010, 10:34 AM
  4. De Moivre's theorem.
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: March 2nd 2009, 07:23 PM
  5. De Moivre's Theorem Question
    Posted in the Pre-Calculus Forum
    Replies: 6
    Last Post: September 13th 2008, 11:53 PM

Search Tags


/mathhelpforum @mathhelpforum