Complex Numbers in Python | Set 2 (Important Functions and Constants)

Introduction to python complex numbers: Complex Numbers in Python | Set 1 (Introduction)
Some more important functions and constants are discussed in this article.
Operations on complex numbers :

1. exp() :- This function returns the exponent of the complex number mentioned in its argument.

2. log(x,b) :- This function returns the logarithmic value of x with the base b, both mentioned in its arguments. If base is not specified, natural log of x is returned.

# Python code to demonstrate the working of
# exp(), log()

# importing "cmath" for complex number operations
import cmath
import math

# Initializing real numbers
x = 1.0
y = 1.0

# converting x and y into complex number
z = complex(x, y);

# printing exponent of complex number
print ("The exponent of complex number is : ", end="")
print (cmath.exp(z))

# printing log form of complex number
print ("The log(base 10) of complex number is : ", end="")
print (cmath.log(z,10))

Output:

The exponent of complex number is : (1.4686939399158851+2.2873552871788423j)
The log(base 10) of complex number is : (0.15051499783199057+0.3410940884604603j)

3. log10() :- This function returns the log base 10 of a complex number.

4. sqrt() :- This computes the square root of a complex number.

# Python code to demonstrate the working of
# log10(), sqrt()
# importing "cmath" for complex number operations
import cmath
import math

# Initializing real numbers
x = 1.0
y = 1.0

# converting x and y into complex number
z = complex(x, y);

# printing log10 of complex number
print ("The log10 of complex number is : ", end="")
print (cmath.log10(z))

# printing square root form of complex number
print ("The square root of complex number is : ", end="")
print (cmath.sqrt(z))

Output:

The log10 of complex number is : (0.15051499783199057+0.3410940884604603j)
The square root of complex number is : (1.09868411346781+0.45508986056222733j)

5. isfinite() :- Returns true if both real and imaginary part of complex number are finite, else returns false.

6. isinf() :- Returns true if either real or imaginary part of complex number is/are infinite, else returns false.

7. isnan() :- Returns true if either real or imaginary part of complex number is NaN , else returns false.

# Python code to demonstrate the working of
# isnan(), isinf(), isfinite()

# importing "cmath" for complex number operations
import cmath
import math

# Initializing real numbers
x = 1.0
y = 1.0
a = math.inf
b = math.nan

# converting x and y into complex number
z = complex(x,y);

# converting x and a into complex number
w = complex(x,a);

# converting x and b into complex number
v = complex(x,b);

# checking if both numbers are finite
if cmath.isfinite(z):
       print ("Complex number is finite")
else : print ("Complex number is infinite")

# checking if either number is/are infinite
if cmath.isinf(w):
       print ("Complex number is infinite")
else : print ("Complex number is finite")

# checking if either number is/are infinite
if cmath.isnan(v):
       print ("Complex number is NaN")
else : print ("Complex number is not NaN")

Output:

Complex number is finite
Complex number is infinite
Complex number is NaN

Constants

There are two constants defined in cmath module, “pi”, which returns the numerical value of pi. The second one is “e” which returns the numerical value of exponent.

# Python code to demonstrate the working of
# pi and e

# importing "cmath" for complex number operations
import cmath
import math

# printing the value of pi
print ("The value of pi is : ", end="")
print (cmath.pi)

# printing the value of e
print ("The value of exponent is : ", end="")
print (cmath.e)

Output:

The value of pi is : 3.141592653589793
The value of exponent is : 2.718281828459045

Complex Numbers in Python | Set 3 (Trigonometric and Hyperbolic Functions)

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