# Plotting the complex exp function in Maple?

1. Apr 18, 2010

### Susanne217

1. The problem statement, all variables and given/known data

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

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 $$e^{i\cdot t} = cos(t) + i \cdot sin(t)$$

Last edited: Apr 18, 2010
2. Apr 18, 2010

### lanedance

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

3. Apr 19, 2010

### Susanne217

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
4. Apr 19, 2010

### lanedance

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 $e^{ix}$ along the y axis, and the imaginary part along the z axis. Then parametrically you would plot
$$x(t) = t$$
$$y(t) = cos(t)$$
$$z(t) = sin(t)$$

and the curve will look like part of a spiral with its central axis along the x axis

5. Apr 19, 2010

### Susanne217

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?

6. Apr 19, 2010

### lanedance

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)

7. Apr 19, 2010

### Susanne217

I thought of something Lanedance.

Since modulus for $$e^{it}$$ where $$0 \leq t \leq 2\pi$$ 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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