Results 1 to 4 of 4

Thread: Solve equation with e for "b"

  1. #1
    Newbie
    Joined
    Sep 2015
    From
    oklahoma
    Posts
    18

    Solve equation with e for "b"

    Could anyone help me with the steps to solve this equation for b ?

    Solve equation with e for "b"-equation.jpg
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    22,155
    Thanks
    3048
    Awards
    1

    Re: Solve equation with e for "b"

    Quote Originally Posted by rickS View Post
    Could anyone help me with the steps to solve this equation for b ?
    Click image for larger version. 

Name:	equation.JPG 
Views:	1 
Size:	13.9 KB 
ID:	38567
    $\exp( i\pi)=-1$
    So you have $(\exp(\pi))^2+b^2=1$
    Can you now find $b~?$
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2015
    From
    oklahoma
    Posts
    18

    Re: Solve equation with e for "b"

    Plato, that is helpful. But I am still a bit lost; what if it is an "x" instead of pi:
    Solve equation with e for "b"-equation.jpg


    Such that we cannot use exp(ipi) = -1
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    22,155
    Thanks
    3048
    Awards
    1

    Re: Solve equation with e for "b"

    Quote Originally Posted by rickS View Post
    Plato, that is helpful. But I am still a bit lost; what if it is an "x" instead of pi:
    Click image for larger version. 

Name:	equation.JPG 
Views:	0 
Size:	13.9 KB 
ID:	38570
    Such that we cannot use exp(ipi) = -1
    @rickS, the new equation is $\large\left(e^{ix}\right)^2=\large\left(e^{x} \right)^2+b^2$, solve for $x$.
    Now we have a very difficult problem. Whole courses a devoted to the study of theory of equations. And courses on numerical methods.

    Here is a sample from the above: $\left(e^{ix}\right)^2=\left(e^{i(2x)}\right)=\cos (2x)+{\bf{i}} \sin(2x)$

    I hope you can the difficulty solving for $x$ in: $\cos(2x)+{\bf{i}} \sin(2x)=e^{2x}+b^2~?$
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: Apr 24th 2011, 08:01 AM
  2. Replies: 1
    Last Post: Oct 25th 2010, 05:45 AM
  3. Replies: 5
    Last Post: Sep 19th 2010, 12:10 AM
  4. Solve differential equation using "Power Series"
    Posted in the Differential Equations Forum
    Replies: 22
    Last Post: Jul 25th 2010, 08:47 AM
  5. Replies: 1
    Last Post: Jun 4th 2010, 11:26 PM

/mathhelpforum @mathhelpforum