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
# Python code to demonstrate the working of# complex(), real() and imag()# importing "cmath" for complex number operationsimport cmath# Initializing real numbersx = 5y = 3# converting x and y into complex numberz = complex(x,y);# printing real and imaginary part of complex numberprint ("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
An alternative way to initialize a complex number
Below is the implementation of how can we make complex no. without using complex() function
Python3
# Aleternative way how can complex no can initialize# importing "cmath" for complex number operationsimport cmath# Initializing complex numberz = 5+3j# Print the parts of Complex No.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
Explanation: Phase of complex number Geometrically, the phase of a complex number is the angle between the positive real axis and the vector representing a complex number. This is also known as the argument of a complex number. Phase is returned using phase(), which takes a complex number as an argument. The range of phase lies from -pi to +pi. i.e from -3.14 to +3.14.
Python
# Python code to demonstrate the working of# phase()# importing "cmath" for complex number operationsimport cmath# Initializing real numbersx = -1.0y = 0.0# converting x and y into complex numberz = 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
# Python code to demonstrate the working of# polar() and rect()# importing "cmath" for complex number operationsimport cmathimport math# Initializing real numbersx = 1.0y = 1.0# converting x and y into complex numberz = complex(x,y);# converting complex number into polar using polar()w = cmath.polar(z)# printing modulus and argument of polar complex numberprint ("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 numberprint ("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) This article is contributed by Manjeet Singh. If you like Lazyroar and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the Lazyroar main page and help other Geeks. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
