# 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 num)

  Return the negation of the complex number num, 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`.

## 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`. This function always succeeds.

int `PyComplex_CheckExact`(PyObject *p)

  Return true if its argument is a `PyComplexObject`, but not a subtype of `PyComplexObject`. This function always succeeds.

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.