Complex Number Objects
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.

Py_complex _Py_c_pow(Py_complex num, Py_complex exp)
 Return the exponentiation of num by exp, using the C Py_complex
representation.
Complex Numbers as Python Objects

PyComplexObject
 This subtype of PyObject represents a Python complex number object.

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

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

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

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.

double PyComplex_RealAsDouble(PyObject *op)
 Return the real part of op as a C double.

double PyComplex_ImagAsDouble(PyObject *op)
 Return the imaginary part of op as a C double.

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.