Complex numbers¶
Complex numbers consist of a real part and an imaginary part, which is given the suffix
j in Python.
>>> 7 + 2j
(7+2j)
Note
Python expresses the resulting complex number in parentheses to indicate that the output represents the value of a single object:
>>> (5 + 3j) ** (3 + 5j)
(-7.04464115622119-11.276062812695923j)
>>> x = (5 + 3j) * (6 + 8j)
>>> x
(6+58j)
>>> x.real
6.0
>>> x.imag
58.0
Complex numbers consist of a real part and an imaginary part with the suffix
j. In the preceding code, the variable x is assigned to a complex
number. You can get its „real“ part with the attribute notation x.real and
the „imaginary“ part with x.imag.
Advanced functions¶
The functions in the math module are not
applicable to complex numbers; one of the reasons for this is probably that the
square root of -1 is supposed to produce an error. Therefore, similar
functions for complex numbers have been provided in the cmath module:
cmath.acos(), cmath.acosh(), cmath.asin(), cmath.asinh(), cmath.atan(), cmath.atanh(), cmath.cos(), cmath.cosh(), python3:cmath.e(), cmath.exp(), cmath.log(), cmath.log10(), python3:cmath.pi(), cmath.sin(), cmath.sinh(), cmath.sqrt(), cmath.tan(), cmath.tanh().
To make it clear in the code that these functions are special functions for
complex numbers, and to avoid name conflicts with the more normal equivalents,
it is recommended to simply import the module to explicitly refer to the
cmath package when using the function, for example:
>>> import cmath
>>> cmath.sqrt(-2)
1.4142135623730951j
Warning
Now it becomes clearer why we do not recommend importing all functions of a
module with from MODULE import *. If you would import the module
math first and then the module cmath, the functions in cmath
would have priority over those of math. Also, when understanding the
code, it is much more tedious to find out the source of the functions used.