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)

This article is contributed by **Manjeet Singh**. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

Attention geek! Strengthen your foundations with the **Python Programming Foundation** Course and learn the basics.

To begin with, your interview preparations Enhance your Data Structures concepts with the **Python DS** Course.