I’m a math newbie. Now I’m getting deeper into Python data types. I can’t understand how to use a complex number. Please give me examples of usage of complex numbers in Python.

In python, you can put ‘j’ or ‘J’ after a number to make it imaginary, so you can write complex literals easily:

>>> 1j
1j
>>> 1J
1j
>>> 1j * 1j
(-1+0j)

The ‘j’ suffix comes from electrical engineering, where the variable ‘i’ is usually used for current. (Reasoning found here.)

The type of a complex number is complex, and you can use the type as a constructor if you prefer:

>>> complex(2,3)
(2+3j)

A complex number has some built-in accessors:

>>> z = 2+3j
>>> z.real
2.0
>>> z.imag
3.0
>>> z.conjugate()
(2-3j)

Several built-in functions support complex numbers:

>>> abs(3 + 4j)
5.0
>>> pow(3 + 4j, 2)
(-7+24j)

The standard module cmath has more functions that handle complex numbers:

>>> import cmath
>>> cmath.sin(2 + 3j)
(9.15449914691143-4.168906959966565j)

The following example for complex numbers should be self explanatory including the error message at the end

>>> x=complex(1,2)
>>> print x
(1+2j)
>>> y=complex(3,4)
>>> print y
(3+4j)
>>> z=x+y
>>> print x
(1+2j)
>>> print z
(4+6j)
>>> z=x*y
>>> print z
(-5+10j)
>>> z=x/y
>>> print z
(0.44+0.08j)
>>> print x.conjugate()
(1-2j)
>>> print x.imag
2.0
>>> print x.real
1.0
>>> print x>y

Traceback (most recent call last):
  File "<pyshell#149>", line 1, in <module>
    print x>y
TypeError: no ordering relation is defined for complex numbers
>>> print x==y
False
>>>