Pythonâ€™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.

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`

to`EDOM`

.

- 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`

to`EDOM`

.

`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. If`__complex__()`

is not defined then it falls back to`__float__()`

. If`__float__()`

is not defined then it falls back to`__index__()`

. Upon failure, this method returns`-1.0`

as a real value.Changed in version 3.8: Use

`__index__()`

if available.