Results 1 to 3 of 3

Math Help - squaring exponentials

  1. #1
    Senior Member
    Joined
    Oct 2008
    Posts
    393

    squaring exponentials

    is (e^(i \theta))(e^(i \theta)) =  e^(2i \theta))
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jun 2009
    From
    United States
    Posts
    676
    Thanks
    19
    Yes, it is true. You have the two formulae:

    e^{i\theta}=cos(\theta)+isin(\theta)

    For 2\theta

    e^{i(2\theta)}=cos(2\theta)+isin(2\theta)

    You can show that your equation is true as follows:

    (e^{i\theta})(e^{i\theta})

    =\left[cos(\theta)+isin(\theta)\right]\left[cos(\theta)+isin(\theta)\right]

    =cos^2(\theta)+2isin(\theta)cos(\theta)+i^2sin^2(\  theta)

    Remember:

    i^2=-1

    So the equation simplifies to:

    =cos(2\theta)+isin(2\theta)

    =e^{i(2\theta)}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,915
    Thanks
    1762
    Awards
    1
    Quote Originally Posted by adam_leeds View Post
    is (e^{i \theta})(e^{i \theta}) =  e^{2i \theta})
    Yes it is.

    BTW. See how I fixed the exponents is the LaTeX.
    [tex] e^{2i \theta}[/tex] gives  e^{2i \theta}.
    Note the braces about the exponents with more that one character.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Squaring the circle
    Posted in the Geometry Forum
    Replies: 7
    Last Post: February 15th 2011, 06:12 PM
  2. Squaring numbers
    Posted in the Algebra Forum
    Replies: 5
    Last Post: December 29th 2010, 06:36 PM
  3. Squaring Radicals
    Posted in the Algebra Forum
    Replies: 4
    Last Post: December 1st 2009, 03:20 PM
  4. Squaring radicals
    Posted in the Algebra Forum
    Replies: 3
    Last Post: September 4th 2008, 03:58 PM
  5. Squaring a fraction
    Posted in the Algebra Forum
    Replies: 2
    Last Post: June 30th 2008, 06:14 PM

Search Tags


/mathhelpforum @mathhelpforum