Python have **five built-in data types** one of which is **Numbers**, now as numbers can be integers, floats or complex. Doing mathematics on these require different functions because **you cannot mathematically treat intergers/float in the same way as Complex Numbers** because these have an imaginary part while integers/floats don’t.

Owing to this reason, Python’s core developers have put together two modules containing Mathematical Functions.

• **cmath module **for Complex Numbers

• **math module** for all other types of numbers

**How to import cmath in Python?** You can import python’s cmath module into code by using **import cmath** statement and to access functions inside it do cmath.function_name(parameter).

If your unaware of Python’s Math Module then you can see – Math Module in Python Programming Language article which I put up on this website some days back.

Below are some tables explaining **what are functions there inside cMath Module?** with some examples for each.

**Stop 🖐🏻****What are Complex Numbers?** 🤷🏻 Those numbers which are made up of two parts – Real and Complex. And have form like **a + b**i where both a, b are real numbers while **i is iota = √ -1** (Square root of -1).

Note – Complex numbers are not real but real number can be complex. Like if in **a + bi, b = 0** then we will have **a + 0i** which is both real, complex.**That’s why functions in cMath Module can be applied to Integers/Floats as well but functions in Math Module can’t be applied to Complex Numbers.**

**How to create Complex Number in Python?** For having simple numbers in Python, you just need to type it like 3, 2, 29. But owing to specific syntax of complex numbers **a + bj**. You need to you complex(a, b) constructor for creating these in Python, as **a + bj** will be considered just a String by Python Interpreter.

**Just a Fact**

In mathematics imaginary number is denoted by **i (iota)** but in Python conventionally its denoted by **j**

Table of Contents

## Examples of using cmath Module in Python Code

```
# Firstly import cmath module
import cmath
# Printing Mathematical constants Pie, Square root of -1 iota
print(cmath.pi)
print(cmath.sqrt(-1))
# Above code outputs
3.141592653589793
1j
```

## Conversion Functions in cMath Module

Function | Description |
---|---|

cmath.phase(x) | Returns phase of x as a float. For example – cmath.phase(complex(10, 2)) will return 0.19739555984988075 |

cmath.polar(x) | Return representation of x as polar coordinates. For example – cmath.phase(complex(10, 2)) will return 0.19739555984988075 |

cmath.rect(r, phi) | Return the complex number x with polar coordinates r and phi. Equivalent to r * (math.cos(phi) + math.sin(phi)* i) here i is iotaFor example – cmath.rect(4,16) will return (-3.8306379212935386-1.1516132666602612j) |

**Diagram showing what’s cmath.phase() in Python?**

## Logarithmic Functions in cMath Python Module

Function | Description |
---|---|

cmath.exp(x) | Return e raised to power x – e^{x} .For example – cmath.exp(complex(10, 2)) will return (-9166.244060822655+20028.608669281643j) |

cmath.log(x, base) | If base is not defined then returns natural logarithm of x, otherwise returns log of x to a specified base. For example – cmath.log10(complex(19, 2)) will return (1.2811464322282373+0.04554747576944601j) |

cmath.log10(x) | Returns logarithm of x with base being 10. For example – cmath.log10(complex(3, 5)) will return (0.7657394585211276+0.44748697004049304j) |

cmath.sqrt(x) | Returns square root of x. For example – cmath.sqrt(complex(29, 29)) will return (5.916595022004622+2.4507339011834555j) |

## Trigonometric Functions in cMath Python Module

Function | Description |
---|---|

cmath.sin(x) | Returns sine of complex number x. For example – cmath.sin(complex(28, 3)) will return (2.7273879093833497-9.643265173120367j) |

cmath.cos(x) | Returns cosine of complex number x. For example – cmath.cos(complex(28, 3)) will return (-9.691190497197827-2.713900304379616j) |

cmath.tan(x) | Returns tangent of complex number x. For example – cmath.tan(complex(28, 3)) will return (-0.002574685032008448+0.9957757629883296j) |

## Constants in cMath Python Module

Function | Description |
---|---|

cmath.pi | Returns mathematical constant π = 3.141592 |

cmath.e | Returns mathematical exponent value e = 2.718281 |

cmath.tau | Returns mathematical constant value τ = 6.283185 |

cmath.nan | Returns non a number NaN |

cmath.inf | Floating point positive infinity |

cmath.infj | Complex number a + bj where a = 0 and b = ∞ |

cmath.nanj | Complex number a + bj where a = 0 and b = NaN |

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