Plotting the graph on the complex plain
Question: I would like to plot the graphic of function: `w(s) = 1/(1+s)`.

`s` is the product of the imaginary unit (`1j`) and the variable called
`omega`; i.e. `s = 1j*omega`.

How I can plot that in the complex axis (Real and Imaginary) using Python (2.7
or 3.4) and `matplotlib`?


Answer: You're not clear in your question about what you want to plot, but assuming
omega = x + iy is the number you wish to plot w(s) as a function of, you have
to decide how to present the complex numbers w(s). You might choose a plot
with Cartesian axes representing the real (x) and imaginary (y) axes and to
plot the absolute value of w(s) as a colour, or you might choose to plot the
real and imaginary parts separately. For example,

    
    
    import matplotlib as plt
    import numpy as np
    
    x = np.linspace(-0.5,0.5,100)
    y = np.linspace(-3,0,100)
    X, Y = np.meshgrid(x,y)
    
    def f(x, y):
        return 1./(1+1j*(x+1j*y))
    
    import pylab
    pylab.imshow(np.abs(f(X,Y)))
    pylab.show()
    

[![enter image description
here](http://i.stack.imgur.com/qrjuS.png)](http://i.stack.imgur.com/qrjuS.png)

