 # Complex Numbers in Python | Kit 1 (Introduction)

Converting real numbers to complex numbers

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

 ` # Python code to demonstrate how it works ` ` # complex (), real () and imag () `   ` # import & quot; cmath & quot; for operations with complex numbers ` ` import ` ` cmath `   ` # Initializing real numbers ` ` x ` ` = ` ` 5 ` ` y ` ` = ` ` 3 `   ` # convert x and y to complex number ` ` z ` ` = complex (x, y); ````   # printing real and imaginary parts of a 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     Complex phase th number    Geometrically, the phase of a complex number — it is the  angle between the positive real axis and the vector representing the complex number . This is also known as the  argument  of a complex number. Phase is returned by  phase () , which takes a complex number as an argument. The phase range is from  -pi to + pi.  that is, from  -3.14 to +3.14 .           ` # Python code to demonstrate how it works `  ` # phase () `     ` # import & quot; cmath & quot; for operations with complex numbers `   ` import ` ` cmath `    ` # Initializing real numbers `   ` x ` ` = ` ` - ` ` 1.0 `   ` y ` ` = ` ` 0.0 `     ` # convert x and y to complex number `   ` z   =   complex   (x, y); ``     # printing the 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

Conversion from polar to rectangular and vice versa
Conversion to polar is performed using  polar () , which returns a  pair (r, ph),  denoting  module r  and phase  angle ph . a module can be rendered using  abs (),  and a phase using  phase () .  A complex number is converted to rectangular coordinates using  rect (r, ph) , where  r — module,  and  ph — phase angle . Returns a value numerically  r * (math.cos (ph) + math.sin (ph) * 1j)

` # Python code to demonstrate how it works `  ` # polar () and rect () `
` # import & quot; cmath & quot; for operations with complex numbers `
` import ` ` cmath `
` import ` ` math `
` # Initializing real numbers `
` x ` ` = ` ` 1.0 `
` y ` ` = ` ` 1.0 `
` `  ` # convert x and y to complex number  ````
z   =   complex   (x, y);
# convert complex number to polar using polar ()
w   =   cmath.polar (z)
# print engine and polar complex number argument
print   (  "The modulus and argument of polar complex number is:"  , end   =   "")
print   (w)
# convert complex number to rectangular using rect ()
w   =   cmath.rect (  1.4142135623730951  ,   0.7853981633974483  )
# printing a rectangular 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)
Manjit Singh  . If you are as Python.Engineering and would like to contribute, you can also write an article using  contribute.python.engineering  or by posting an article contribute @ python.engineering. See my article appearing on the Python.Engineering homepage and help other geeks.