# 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.

type 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.

  double real
  double imag

  The structure 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`.

  Set `errno` to `ERANGE` on overflows.

## Complex Numbers as Python Objects

type PyComplexObject

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

PyTypeObject PyComplex_Type
  Part of the Stable ABI.

  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. Return `NULL` with an exception set on error.

PyObject *PyComplex_FromDoubles(double real, double imag)
  Return value: New reference. Part of the Stable ABI.

  Return a new `PyComplexObject` object from real and imag. Return `NULL` with an exception set on error.

double PyComplex_RealAsDouble(PyObject *op)
  Part of the Stable ABI.

  Return the real part of op as a C double.

  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 call `PyFloat_AsDouble()` and returns its result.

  Upon failure, this method returns `-1.0` with an exception set, so one should call `PyErr_Occurred()` to check for errors.

  Changed in version 3.13: Use `__complex__()` if available.

double PyComplex_ImagAsDouble(PyObject *op)
  Part of the Stable ABI.

  Return the imaginary part of op as a C double.

  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 call `PyFloat_AsDouble()` and returns `0.0` on success.

  Upon failure, this method returns `-1.0` with an exception set, so one should call `PyErr_Occurred()` to check for errors.

  Changed in version 3.13: Use `__complex__()` if available.

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 `Py_complex` with `real` set to `-1.0` and with an exception set, so one should call `PyErr_Occurred()` to check for errors.

  Changed in version 3.8: Use `__index__()` if available.