I am trying to make a conformal plot of complex functions using contours in python using Matplotlib and NumPy. The thing is, whenever I run the code I get a plot for the inverse function.
For example, say I want to plot $f(z) = z^{2}$ : I would use this code:
import numpy as np
def f(z):
return z**2 #definig function as x^2
x = np.linspace(-4,4,100) #real part of input
y = np.linspace(-4,4,100) #imaginary part of input
X,Y = np.meshgrid(x,y)
w = f(X + 1j*Y) #Plugging the real and imaginary parts into the function
plt.contour(X,Y, np.real(w)) #plots contour with the real part of the output
plt.contour(X,Y, np.imag(w)) #plots contour with the real part of the output
plt.show()
This gives me this picture:
The problem is that is the plot of the inverse function $f^{-1}(z) = \sqrt{z}$.
The picture I should have gotten should look like this:
I got that picture by changing $f(z)$ from $z^2$ to $\sqrt{z}$. I have had this problem with every function I have tried including $sin(z), \ exp(z), \ x^3$ and various other polynomials. Aside from this, I have genuinely no idea what to do or where to go from here. nor do I know what the problem actually is.
Note: I have not take complex analysis before so I dont have much knowledge about the subject so sorry if I misuse any terminology. The main reason I am doing any of this is because I think the plots look pretty. My main reference for how the plots should look is this geogebra project I made a while ago: https://www.geogebra.org/m/phmtsgrf
Why do you think the first plot is plot for the inverse function? It looks like the correct plot for $f(z)$ to me.
For example, $Re f(z) = Re (x+iy)^2 = x^2 - y^2$ so the contours should be curves of the form $x^2 - y^2 = c$. That's exactly what the first plot looks like to me.