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

Introduction to python complex numbers: Complex Numbers in Python | Set 1 (Introduction)
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)

Python