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.

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