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)
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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
>>>
It appears to be, as you guessed, because Python follows the electrical engineering convention. Here's an exchange from the Python bug tracker Issue10562:
Boštjan Mejak: In Python, the letter 'j' denotes the imaginary unit. It would be great if we would follow mathematics in this regard and let the imaginary unit be denoted with an 'i'.
Michael Foord: We follow engineering which uses j.
(I was about to close this as wontfix but Antoine is particularly keen that Mark deals with this issue...)
Mark Dickinson: Just to add my own thoughts: 'j' for a (not the ) square root of -1 has, as Michael points out, a history of use in engineering (particularly electrical engineering) and physics. Personally, I would have preferred 'i' to 'j' here, but changing it now would cause (IMO) gratuitous breakage. It really doesn't seem a big enough issue to be worth making a fuss about.
...
Much later:
Guido van Rossum: This will not be fixed. For one thing, the letter 'i' or upper case 'I' look too much like digits. The way numbers are parsed either by the language parser (in source code) or by the built-in functions (int, float, complex) should not be localizable or configurable in any way; that's asking for huge disappointments down the road. If you want to parse complex numbers using 'i' instead of 'j', you have plenty of solutions available already.
Python adopted the convention used by electrical engineers. In that field, i is used to represent current and use j as the square root of -1.
There was a bug logged to change it to i in Python 3.3. It was resolves as a "WONTFIX" with this reasoning by Guido van Rossum:
This will not be fixed. For one thing, the letter 'i' or upper case 'I' look too much like digits. The way numbers are parsed either by the language parser (in source code) or by the built-in functions (int, float, complex) should not be localizable or configurable in any way; that's asking for huge disappointments down the road. If you want to parse complex numbers using 'i' instead of 'j', you have plenty of solutions available already.