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Find the real part

  1. Jun 1, 2014 #1
    Hello, everyone.

    Can some help me finish this solution? I am stuck. The questions is to find the real part of
    i*sin(∏/4 + i).
     

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  2. jcsd
  3. Jun 1, 2014 #2

    LCKurtz

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    Use ##e^{i\theta} = \cos \theta + i\sin\theta## and its conjugate with ##\theta = i##.
     
  4. Jun 1, 2014 #3
    Which part should I use that? I don't get it.
     
  5. Jun 1, 2014 #4

    LCKurtz

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    Solve the Euler equations for ##e^{i\theta}## and ##e^{-i\theta}## for the sine and cosine in terms of the exponentials. Surely your book has those formulas.
     
  6. Jun 1, 2014 #5
    Does that mean I didn't have to use the trig identity?
     
  7. Jun 1, 2014 #6

    LCKurtz

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    You just need ##\sin i## and ##\cos i## to finish, don't you? You can get them from the above formulas.
     
  8. Jun 1, 2014 #7
    Err...you mean like this? But it gets complicated.
     

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  9. Jun 1, 2014 #8
    Wait, I think I got it. Hold on, let me try and solve it and I will show it you.
     
  10. Jun 1, 2014 #9
    Is this correct?
     

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  11. Jun 1, 2014 #10

    LCKurtz

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    That looks correct. Notice that you could have substituted the exponentials for ##\sin(\frac \pi 4 + i)## directly, avoiding using the addition formulas.
     
  12. Jun 1, 2014 #11
    How to substitute the exponentials for ##\sin(\frac \pi 4 + i)## directly?
     
  13. Jun 1, 2014 #12

    LCKurtz

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    ##\sin \theta = \frac {e^{i\theta}-e^{-i\theta}}{2i}##, the same formula you used before.
     
  14. Jun 1, 2014 #13
    You mean like this? But then how do I finish it? Looks complicated there.
     

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  15. Jun 1, 2014 #14

    SammyS

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    attachment.php?attachmentid=70243&d=1401677421.jpg

    What happened to ##\ i\ ## in the denominator?

    Do you know what ##\ e^{i\pi/4}\ ## is ?
     
  16. Jun 1, 2014 #15
    I forgot to write the i.
    ##\ e^{i\pi/4}\ is equals to cos∏/4 + isin∏/4, right? And that makes it equals to 1/√2 + i/√2, right?
     
  17. Jun 1, 2014 #16

    SammyS

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    Yes, and ##\ e^{-i\pi/4}= \ ? ##
     
  18. Jun 1, 2014 #17
    Thanks, I got it!!!!Yay! Thank you!
     
    Last edited: Jun 2, 2014
  19. Jun 2, 2014 #18

    SammyS

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    Good!!
     
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