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Homework Help: Plotting the complex exp function in Maple?

  1. Apr 18, 2010 #1
    1. The problem statement, all variables and given/known data

    If we have [tex]y(x) = e^{i\cdot x}[/tex] where [tex]x\in [0,\pi][/tex]

    How do I plot function in Maple? So it shows anything?


    3. The attempt at a solution
    if I write

    Code (Text):

    plot(exp(I*x),x=0..Pi);
     
    I get an empty coordinate system. Do I need to add some more code to get it to display properly?

    Sincerely
    Susanne

    p.s. I know [tex]e^{i\cdot t} = cos(t) + i \cdot sin(t)[/tex]
     
    Last edited: Apr 18, 2010
  2. jcsd
  3. Apr 18, 2010 #2

    lanedance

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    what do you hope to see - note if you're trying to do a 2D plot have you thought through how you can even plot a complex function?

    a 2D plot is generally a scalar function of a single variable

    it might be better to plot the magnitude and phase or the real and imaginary parts which are each scalars so can be plotted in 2D against x
     
  4. Apr 19, 2010 #3
    So what I do here is that I take the real part of complex exp function and plot it along the x-axis and imaginary part along the y-axis?

    where cos(t) is real part and i*sin(t) the img part.

    EDIT: I plot the real part cos(t) along the interval zero to Pi that gives the real Cosine function while the imaginary part along the same interval i*sin(t) me nothing.

    Can that be right? because i*sin(0) = 0 and i*sin(Pi) =0.

    So all in the plot of complex exp function along the interval [0,Pi] is simply the real cosine function?
     
    Last edited: Apr 19, 2010
  5. Apr 19, 2010 #4

    lanedance

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    you have to decide what you want to plot... i can't tell you what it is you want to do...

    but...if you have a complex number z = a + ib, then a & b are both scalars, a is the real part, & b is the imaginary part.

    hence why you can't plot isin(x), that is still a complex number, to plot the imaginary part you just plot sin(t).

    if you want x to vary in the interval and plot the real part of [itex] e^{ix} [/itex] along the y axis, and the imaginary part along the z axis. Then parametrically you would plot
    [tex] x(t) = t[/tex]
    [tex] y(t) = cos(t)[/tex]
    [tex] z(t) = sin(t)[/tex]

    and the curve will look like part of a spiral with its central axis along the x axis
     
  6. Apr 19, 2010 #5
    I may have a whole in my knowledge so please excuse me :) But the reason that I only need to plot the the scalars a and b of z= cos(t) + i*sin(t) is its impossible to view i*sin(t) as a point by itself graphically?

    Why must I do a 3D plot? Can't I do a 2D plot?
     
  7. Apr 19, 2010 #6

    lanedance

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    once again you can do whatever you want, you just have to decide - you could plot both the real and imaginary part of the function as 2 separate curves in 2D... on the same graph even

    you can't plot i.sin(t) as its a complex number, you can decide an axis will represent the imaginary part of a complex number, but the plot command you give will be a scalar function

    you can plot any scalar function, as said, examples of scalar function of a compelx variable are:
    - real part
    - imaginary part
    - magnitude
    - phase (arg)
     
  8. Apr 19, 2010 #7
    I thought of something Lanedance.

    Since modulus for [tex]e^{it}[/tex] where [tex]0 \leq t \leq 2\pi[/tex] is one..

    Then can't a plot of exp(it) as show in my file attachment. Don't know howto show something simular in Maple...
     

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