# Complex numbers in python

## Question:

Are complex numbers a supported data-type in Python? If so, how do you use them?

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
>>>
``````

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)
``````

Yes, complex type is supported in Python.

For numbers, Python 3 supports 3 types int, float and complex types as shown below:

``````print(type(100), isinstance(100, int))
print(type(100.23), isinstance(100.23, float))
print(type(100 + 2j), isinstance(100 + 2j, complex))
``````

Output:

``````<class 'int'> True
<class 'float'> True
<class 'complex'> True
``````

For numbers, Python 2 supperts 4 types int, long, float and complex types as shown below:

``````print(type(100), isinstance(100, int))
print(type(10000000000000000000), isinstance(10000000000000000000, long))
print(type(100.23), isinstance(100.23, float))
print(type(100 + 2j), isinstance(100 + 2j, complex))
``````

Output:

``````(<type 'int'>, True)
(<type 'long'>, True)
(<type 'float'>, True)
(<type 'complex'>, True)
``````

how would you multiply by j in code ?

x = j*(2 + 3j)
Traceback (most recent call last):
File "", line 1, in
NameError: name ‘j’ is not defined

do i really need:

x = complex(0,1)*(2 + 3j)

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