Results 1 to 2 of 2

Math Help - Finding the real parts of this equation

  1. #1
    Newbie
    Joined
    Oct 2012
    From
    Lancaster
    Posts
    20

    Finding the real parts of this equation

    Finding the real parts to both sides of this equation
    I am really stuck trying to find the real parts to both sides of this equation.
    1 + exp(theta(i)) + exp(2theta(i)) + .... + exp((n-1)theta(i)) = (exp(ntheta(i)) - 1) / (exp(theta(i)) -1)


    I think that the real part of the left hand side is
    1 + cos(theta) + cos(2theta) + ..... + cos((n-1)theta)


    i have no idea what the real part is for the right.


    Someone please help
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,589
    Thanks
    1445

    Re: Finding the real parts of this equation

    Quote Originally Posted by Matt1993 View Post
    Finding the real parts to both sides of this equation
    I am really stuck trying to find the real parts to both sides of this equation.
    1 + exp(theta(i)) + exp(2theta(i)) + .... + exp((n-1)theta(i)) = (exp(ntheta(i)) - 1) / (exp(theta(i)) -1)


    I think that the real part of the left hand side is
    1 + cos(theta) + cos(2theta) + ..... + cos((n-1)theta)


    i have no idea what the real part is for the right.


    Someone please help
    I agree with the answer to your LHS. As for the RHS,

    \displaystyle \begin{align*} \frac{e^{n\theta i} - 1}{e^{\theta i} - 1} &= \frac{\cos{(n\theta)} + i\sin{(n\theta)} - 1}{\cos{(\theta)} + i\sin{(\theta)} - 1} \\ &= \frac{\left[ \cos{(n\theta)} - 1 + i\sin{(n\theta )} \right] \left[\cos{(\theta)} - 1 - i\sin{(\theta)}\right]}{\left[ \cos{(\theta )} - 1 + i\sin{(\theta )} \right] \left[ \cos{(\theta )} - 1 - i\sin{(\theta )} \right]} \end{align*}

    Now simplify...
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: November 6th 2012, 04:09 AM
  2. [SOLVED] Real and Imaginary parts
    Posted in the Trigonometry Forum
    Replies: 0
    Last Post: January 6th 2011, 03:34 PM
  3. real and imaginary parts of tan(z)
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 17th 2009, 05:58 AM
  4. Replies: 5
    Last Post: May 6th 2009, 05:50 PM
  5. Real / Imaginary Parts
    Posted in the Algebra Forum
    Replies: 2
    Last Post: February 28th 2009, 10:30 PM

Search Tags


/mathhelpforum @mathhelpforum