Python’s complex number objects are implemented as two distinct types when viewed from the C API: one is the Python object exposed to Python programs, and the other is a C structure which represents the actual complex number value. The API provides functions for working with both.
Complex Numbers as C Structures¶
Note that the functions which accept these structures as parameters and return them as results do so by value rather than dereferencing them through pointers. This is consistent throughout the API.

Py_complex
¶ The C structure which corresponds to the value portion of a Python complex number object. Most of the functions for dealing with complex number objects use structures of this type as input or output values, as appropriate. It is defined as:
typedef struct { double real; double imag; } Py_complex;

Py_complex
_Py_c_sum
(Py_complex left, Py_complex right)¶ Return the sum of two complex numbers, using the C
Py_complex
representation.

Py_complex
_Py_c_diff
(Py_complex left, Py_complex right)¶ Return the difference between two complex numbers, using the C
Py_complex
representation.

Py_complex
_Py_c_neg
(Py_complex complex)¶ Return the negation of the complex number complex, using the C
Py_complex
representation.

Py_complex
_Py_c_prod
(Py_complex left, Py_complex right)¶ Return the product of two complex numbers, using the C
Py_complex
representation.

Py_complex
_Py_c_quot
(Py_complex dividend, Py_complex divisor)¶ Return the quotient of two complex numbers, using the C
Py_complex
representation.If divisor is null, this method returns zero and sets
errno
toEDOM
.

Py_complex
_Py_c_pow
(Py_complex num, Py_complex exp)¶ Return the exponentiation of num by exp, using the C
Py_complex
representation.If num is null and exp is not a positive real number, this method returns zero and sets
errno
toEDOM
.
Complex Numbers as Python Objects¶

PyTypeObject
PyComplex_Type
¶ This instance of
PyTypeObject
represents the Python complex number type. It is the same object ascomplex
in the Python layer.

int
PyComplex_Check
(PyObject *p)¶ Return true if its argument is a
PyComplexObject
or a subtype ofPyComplexObject
.

int
PyComplex_CheckExact
(PyObject *p)¶ Return true if its argument is a
PyComplexObject
, but not a subtype ofPyComplexObject
.

PyObject*
PyComplex_FromCComplex
(Py_complex v)¶  Return value: New reference.
Create a new Python complex number object from a C
Py_complex
value.

PyObject*
PyComplex_FromDoubles
(double real, double imag)¶  Return value: New reference.
Return a new
PyComplexObject
object from real and imag.

Py_complex
PyComplex_AsCComplex
(PyObject *op)¶ Return the
Py_complex
value of the complex number op.If op is not a Python complex number object but has a
__complex__()
method, this method will first be called to convert op to a Python complex number object. Upon failure, this method returns1.0
as a real value.