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E^(i[itex]\omega[/itex]t) question

  1. Nov 15, 2013 #1
    x(t)=e^(i[itex]\omega[/itex]t)

    Is this the correct notation to define this function?

    f:C[itex]\rightarrow[/itex]R

    Does this exponential function take a complex element from the set C and assign to it a real element from the set R?
     
  2. jcsd
  3. Nov 15, 2013 #2

    jedishrfu

    Staff: Mentor

  4. Nov 15, 2013 #3

    D H

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    Staff Emeritus
    Science Advisor

    It's the other way around assuming that ω and t are real. ##f(\omega,t) = e^{i\omega t}## maps ℝ×ℝ to ℂ. (Specifically, to the complex unit circle rather than ℂ in general.)
     
  5. Nov 15, 2013 #4
    Thanks for the replies! D H, is the complex unit circle in the complex plane, meaning that the x axis is the real number line and the y axis is the imaginary number line?
     
  6. Nov 15, 2013 #5

    mathman

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    yes.
     
  7. Nov 16, 2013 #6
    Thanks mathman
     
  8. Nov 16, 2013 #7

    jedishrfu

    Staff: Mentor

    dont for get to thank people via the thanks button
     
  9. Nov 17, 2013 #8
    Ok, thanks for mentioning that jedishrfu
     
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