Not only real numbers, Python can also handle complex numbers and its associated functions using the file “cmath”. Complex numbers have their uses in many applications related to mathematics and python provides useful tools to handle and manipulate them.

**Converting real numbers to complex number**

An complex number is represented by “** x + yi** “. Python converts the real numbers x and y into complex using the function **complex(x,y)**. The real part can be accessed using the function** real()** and imaginary part can be represented by **imag()**.

`# Python code to demonstrate the working of ` `# complex(), real() and imag() ` ` ` `# importing "cmath" for complex number operations ` `import` `cmath ` ` ` `# Initializing real numbers ` `x ` `=` `5` `y ` `=` `3` ` ` `# converting x and y into complex number ` `z ` `=` `complex` `(x,y); ` ` ` `# printing real and imaginary part of complex number ` `print` `(` `"The real part of complex number is : "` `,end` `=` `"") ` `print` `(z.real) ` ` ` `print` `(` `"The imaginary part of complex number is : "` `,end` `=` `"") ` `print` `(z.imag) ` |

Output:

The real part of complex number is : 5.0 The imaginary part of complex number is : 3.0

**Phase of complex number**

Geometrically, the phase of a complex number is the **angle between the positive real axis and the vector representing complex number**. This is also known as** argument **of complex number. Phase is returned using **phase()**, which takes complex number as argument. The range of phase lies from** -pi to +pi.** i.e from **-3.14 to +3.14**.

`# Python code to demonstrate the working of ` `# phase() ` ` ` `# importing "cmath" for complex number operations ` `import` `cmath ` ` ` `# Initializing real numbers ` `x ` `=` `-` `1.0` `y ` `=` `0.0` ` ` `# converting x and y into complex number ` `z ` `=` `complex` `(x,y); ` ` ` `# printing phase of a complex number using phase() ` `print` `(` `"The phase of complex number is : "` `,end` `=` `"") ` `print` `(cmath.phase(z)) ` |

Output:

The phase of complex number is : 3.141592653589793

**Converting from polar to rectangular form and vice versa**

Conversion to polar is done using** polar()**, which returns a **pair(r,ph) ** denoting the **modulus r** and phase **angle ph**. modulus can be displayed using **abs() **and phase using **phase()**.

A complex number converts into rectangular coordinates by using **rect(r, ph)**, where** r is modulus** and** ph is phase angle**. It returns a value numerically equal to **r * (math.cos(ph) + math.sin(ph)*1j)**

`# Python code to demonstrate the working of ` `# polar() and rect() ` ` ` `# 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); ` ` ` `# converting complex number into polar using polar() ` `w ` `=` `cmath.polar(z) ` ` ` `# printing modulus and argument of polar complex number ` `print` `(` `"The modulus and argument of polar complex number is : "` `,end` `=` `"") ` `print` `(w) ` ` ` `# converting complex number into rectangular using rect() ` `w ` `=` `cmath.rect(` `1.4142135623730951` `, ` `0.7853981633974483` `) ` ` ` `# printing rectangular form of complex number ` `print` `(` `"The rectangular form of complex number is : "` `,end` `=` `"") ` `print` `(w) ` |

Output:

The modulus and argument of polar complex number is : (1.4142135623730951, 0.7853981633974483) The rectangular form of complex number is : (1.0000000000000002+1j)

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

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