Results 1 to 4 of 4

Math Help - how come we know that i is 90 degrees or ~1.57 rad?

  1. #1
    Junior Member
    Joined
    Feb 2010
    Posts
    50

    how come we know that i is 90 degrees or ~1.57 rad?

    how come we know that i is 90 degrees or ~1.57 rad

    I cannot understand how come we know this?
    Last edited by mr fantastic; March 26th 2011 at 03:17 PM. Reason: Copied title into main body of post.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Jul 2010
    Posts
    41
    In a way, I've already answered this question today.

    But, in general, when we multiply something by  e^{i\theta} , we rotate it through an angle  \theta in the complex plane.

    Now, if we want to rotate something by  90^o , we would multiply it by  e^{i\frac{\pi}{2}} .

    Now, if you remember that  e^{i\theta} = \cos(\theta) + i \sin(\theta) , and that  \cos(\frac{\pi}{2}) = 0 and  \sin(\frac{\pi}{2}) = 1 .

    Hence...  e^{i \frac{\pi}{2}} = i .
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Feb 2010
    Posts
    50
    Amazing!!! Thanks
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by problady View Post
    how come we know that i is 90 degrees or ~1.57 rad

    I cannot understand how come we know this?
    Review the definition of a radian.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 5
    Last Post: January 13th 2010, 11:50 AM
  2. Degrees
    Posted in the LaTeX Help Forum
    Replies: 2
    Last Post: May 29th 2009, 12:03 AM
  3. Replies: 2
    Last Post: April 6th 2009, 09:19 AM
  4. cot 390 degrees
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: November 6th 2008, 04:36 PM
  5. Sin(45 degrees) / Sec(110 degrees)
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: July 29th 2008, 09:50 PM

Search Tags


/mathhelpforum @mathhelpforum