How to plot complex exponential function in python

sympy has re and im functions:

In [113]: exp(complex(2,1))                                                                          
Out[113]: 
                  1.0⋅ⅈ
7.38905609893065⋅ℯ     

In [114]: re(exp(complex(2,1)))                                                                      
Out[114]: 3.99232404844127

In [115]: im(exp(complex(2,1)))                                                                      
Out[115]: 6.21767631236797

In [116]: exp(complex(2,1)).evalf()                                                                  
Out[116]: 3.99232404844127 + 6.21767631236797⋅ⅈ

.real and .imag are attributes (possibly implemented as properties) of numpy arrays (and complex python numbers).

Exploring sympy a bit more:

In [152]: expand(exp(y),complex=True)                                                                
Out[152]: 
   re(y)               re(y)           
ⅈ⋅ℯ     ⋅sin(im(y)) + ℯ     ⋅cos(im(y))

In [153]: expand(exp(complex(2,1)),complex=True)                                                     
Out[153]: 3.99232404844127 + 6.21767631236797⋅ⅈ

Your sol:

In [157]: sol                                                                                        
Out[157]: 
                 ⎛        ________⎞           ⎛        ________⎞
                 ⎜       ╱  2     ⎟           ⎜       ╱  2     ⎟
             t⋅w⋅⎝-z - ╲╱  z  - 1 ⎠       t⋅w⋅⎝-z + ╲╱  z  - 1 ⎠
x(t) = - C₂⋅ℯ                       + C₂⋅ℯ                      

In [181]: f1 = sol.rhs.subs({w:10, z:0.001,C2:1})                                                    

In [182]: f1                                                                                         
Out[182]: 
   10⋅t⋅(-0.001 - 0.999999499999875⋅ⅈ)    10⋅t⋅(-0.001 + 0.999999499999875⋅ⅈ)
- ℯ                                    + ℯ                                   

Making a numpy compatible function:

In [187]: f = lambdify(t, f1)                                                                        

In [188]: print(f.__doc__)                                                                           
Created with lambdify. Signature:

func(t)

Expression:

-exp(10*t*(-0.001 - 0.999999499999875*I)) + exp(10*t*(-0.001 +...

Source code:

def _lambdifygenerated(t):
    return (-exp(10*t*(-0.001 - 0.999999499999875*1j)) + exp(10*t*(-0.001 + 0.999999499999875*1j)))


Imported modules:

evaluate it at a range of values:

In [189]: f(np.arange(10))                                                                           
Out[189]: 
array([0.+0.j        , 0.-1.07720771j, 0.+1.78972745j, 0.-1.91766624j,
       0.+1.43181934j, 0.-0.49920326j, 0.-0.57406585j, 0.+1.44310044j,
       0.-1.83494157j, 0.+1.63413971j])

same values with just sympy:

In [199]: [im(f1.evalf(subs={t:i})) for i in range(10)]                                              
Out[199]: 
[0, -1.0772077135423, 1.78972744700845, -1.9176662437755, 1.43181934232583, -0.499203257243971, -0.
574065847629935, 1.44310044143674, -1.83494157235822, 1.63413971490123]

Hi, guys today we have got a very easy topic i.e exponential function in Numpy – Python.

So let’s start.

The first question comes in our mind that what is the Exponential Function and what it does?

So as we know about the exponents, this Exponential Function in Numpy is used to find the exponents of  ‘e’.

We know that the value of  ‘e’ is ‘2.71828183’.

If we need to find the exponential of a given array or list, the code is mentioned below.

import numpy as np
#create a list
l1=[1,2,3,4,5]
print(np.exp(l1))

Run this code online

The output of the following code is:-

import numpy as np

l1=np.array([1,2,3,4,5,6,7])
print(l1)
print(np.exp(l1))

Run this program online

The output of the following code is:-

Now the above things are the basics.

Here is the complete syntax of the numpy.exp

numpy.exp(array, out = None, where = True, casting = ‘same_kind’, order = ‘K’, dtype = None)

numpy.exp() with matplotlib

As we know we can plot the graph of ‘e’. Python gives as a special module matplotlib.pyplot.

By using this module we can plot the graph of the ‘e’

Here is the example code for that.

import numpy as np
import matplotlib.pyplot as plt
x= np.array([1,2,3,4,5])
y=np.exp(x)
plt.plot(x,y)
plt.show()

The output of the code is a graph shown below.

Now there is a question arises that what to do if we have to plot two graphs together.

So, no need to worry because we can plot n numbers of the graphs using the module I have mentioned above.

import numpy as np
import matplotlib.pyplot as plt
x= np.array([1,3,5])
y=[2,4,6]
z=np.exp(x)
w=np.exp(y)
plt.plot(x,z,color="blue",marker='*')
plt.plot(y,w,color="red",marker='o')
plt.xlabel("X Axis--------->")
plt.ylabel("Y Axis--------->")
plt.show()

Here is the output of the following code.

So, I hope you have understood this topic very well.

What is complex exponential function?

How do you write imaginary I in Python?

How do I plot a function in Python using MatPlotLib?