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

  1. #1
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    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; Mar 26th 2011 at 03:17 PM. Reason: Copied title into main body of post.
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  2. #2
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    In a way, I've already answered this question today.

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

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

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

    Hence... $\displaystyle e^{i \frac{\pi}{2}} = i $.
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    Amazing!!! Thanks
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  4. #4
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    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.
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