# Complex Number Objects

type PyComplexObject

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

  Py_complex cval

    The complex number value, using the C `Py_complex` representation.

    Deprecated since version 3.15, will be removed in version 3.20: Use `PyComplex_AsCComplex()` and `PyComplex_FromCComplex()` to convert a Python complex number to/from the C `Py_complex` representation.

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_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.

type Py_complex

  This C structure defines an export format for a Python complex number object.

  double real
  double imag

  The structure is defined as:

      typedef struct {
          double real;
          double imag;
      } Py_complex;

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.

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.

## Complex Numbers as C Structures

The API also provides functions for working with complex numbers, using the `Py_complex` representation. 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.

Please note, that these functions are soft deprecated since Python 3.15. Avoid using this API in a new code to do complex arithmetic: either use the Number Protocol API or use native complex types, like double 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.

  Deprecated since version 3.15.

Py_complex _Py_c_diff(Py_complex left, Py_complex right)

  Return the difference between two complex numbers, using the C `Py_complex` representation.

  Deprecated since version 3.15.

Py_complex _Py_c_neg(Py_complex num)

  Return the negation of the complex number num, using the C `Py_complex` representation.

  Deprecated since version 3.15.

Py_complex _Py_c_prod(Py_complex left, Py_complex right)

  Return the product of two complex numbers, using the C `Py_complex` representation.

  Deprecated since version 3.15.

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`.

  Deprecated since version 3.15.

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.

  Deprecated since version 3.15.

double _Py_c_abs(Py_complex num)

  Return the absolute value of the complex number num.

  Set `errno` to `ERANGE` on overflows.

  Deprecated since version 3.15.