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` `)) ` |

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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)) ` |

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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"` `) ` |

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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) ` |

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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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