# Numpy: Complex Equation Curve is Plotted Incorrectly

I am trying to use the Python to do some graphical analysis.

I need to plot this equation:
Where fn is on the x axis (log scale 0 – 10) and Mg is on the y axis.
Ln and Qe are dummy variables that I will enter different values for, but for now I am working with just

``````Ln = 5
Qe = 0.5
`````` The plot is supposed to look something like this:

Mind you I am only trying to plot one value for Qe at this time, so we would only see one curve. Here is the code I have so far:

``````    import numpy as np
import pylab
import matplotlib.pyplot as plt
import math
Ln = 5
Qe = .5
fn = np.linspace(.1, 10, 1000)
Mg_Num = Ln * fn**2
Mg_Dem = ((Ln + 1) * (fn**2 - 1)) + ((fn**2 - 1) * fn * Qe * Ln)
Mg = abs(Mg_Num/Mg_Dem)

plt.plot(fn, Mg)
plt.xscale('log')

plt.show()
``````

And this is the plot it generates: It does not really look like the curve of Ln = 5, Qe = 0.5 (orange curve) in the graph above.

I am thinking maybe it has to do with the imaginary part of Mg in the denominator, but I am not sure how to incorporate that into such a complex equation (no pun intended).

Any suggestions on what I should do?

### >Solution :

You can write complex functions by using `j`.
For example `x = 3 + 5j`.
Besides the imaginary part you had a placed a parenthesis incorrectly.

``````import numpy as np
import matplotlib.pyplot as plt

Ln = 5
Qe = .5
fn = np.linspace(.1, 10, 1000)

Mg_Num = Ln * fn**2
Mg_Dem = ((Ln + 1) *  fn**2 - 1 ) + 1j*((fn**2 - 1) * fn * Qe * Ln)
#                    ^         ^    ^^
Mg = np.abs(Mg_Num / Mg_Dem)

plt.plot(fn, Mg)
plt.xscale('log')
plt.show()
``````