Complex numbers in python

Question

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

As you say you are new to maths, can you write what you you want to do in mathematical notation? — mmmmmm, Dec 03 '11 at 20:15
I don't think this should have been closed. I also found it confusing that python used the 'j' imaginary syntax common in engineering over the more intuitive 'i' syntax common in math, statistics, R, etc. The first answer below did a good job introducing that. — Mittenchops, May 20 '13 at 16:12
It seems a legitimate docbug on Python that `help(complex)` doesn't show any examples, unlike e.g. ` import decimal; help(decimal)` — smci, May 03 '17 at 10:16

score 255 · Accepted Answer · edited May 23 '17 at 12:10

255

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)

edited May 23 '17 at 12:10

Community

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answered Dec 03 '11 at 20:20

rob mayoff

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'i' is also used by mathematicians, physicists, and nearly all other scientists. If that isn't confusing enough, some use 'i' to represent the "positive" square root of one, whereas 'j' is the "negative" square root of one. Thus i == -j. FYJ... – jvriesem Sep 16 '16 at 04:28
2

@jvriesem "the positive square root of one" is one. Do you mean they use `i` to represent the positive square root of *negative* one? and `j` to represent the negative square root of *negative* one? – joseville Oct 12 '21 at 03:35
The i/j argument for current is a bit weak, j is used for current density. – copper.hat Jul 03 '23 at 21:45

score 18 · Answer 2 · answered Dec 03 '11 at 20:18

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
>>>

Super Kai - Kazuya Ito · Answer 3 · 2022-11-24T11:00:12.317

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)

Complex numbers in python

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