diff --git a/spec/2022.12/API_specification/array_object.rst b/spec/2022.12/API_specification/array_object.rst
index b15bbdc43..45aec9b34 100644
--- a/spec/2022.12/API_specification/array_object.rst
+++ b/spec/2022.12/API_specification/array_object.rst
@@ -163,7 +163,8 @@ A conforming implementation of the array API standard must provide and support a
     -   `operator.ne(x1, x2) <https://docs.python.org/3/library/operator.html#operator.ne>`_
     -   `operator.__ne__(x1, x2) <https://docs.python.org/3/library/operator.html#operator.__ne__>`_
 
-Comparison operators should be defined for arrays having any data type.
+:meth:`.array.__lt__`, :meth:`.array.__le__`, :meth:`.array.__gt__`, :meth:`.array.__ge__` are only defined for arrays having real-valued data types. Other comparison operators should be defined for arrays having any data type.
+For backward compatibility, conforming implementations may support complex numbers; however, inequality comparison of complex numbers is unspecified and thus implementation-dependent (see :ref:`complex-number-ordering`).
 
 In-place Operators
 ~~~~~~~~~~~~~~~~~~
diff --git a/spec/draft/API_specification/array_object.rst b/spec/draft/API_specification/array_object.rst
index 0fadf9fc5..f8a586ade 100644
--- a/spec/draft/API_specification/array_object.rst
+++ b/spec/draft/API_specification/array_object.rst
@@ -163,7 +163,8 @@ A conforming implementation of the array API standard must provide and support a
     -   `operator.ne(x1, x2) <https://docs.python.org/3/library/operator.html#operator.ne>`_
     -   `operator.__ne__(x1, x2) <https://docs.python.org/3/library/operator.html#operator.__ne__>`_
 
-Comparison operators should be defined for arrays having any data type.
+:meth:`.array.__lt__`, :meth:`.array.__le__`, :meth:`.array.__gt__`, :meth:`.array.__ge__` are only defined for arrays having real-valued data types. Other comparison operators should be defined for arrays having any data type.
+For backward compatibility, conforming implementations may support complex numbers; however, inequality comparison of complex numbers is unspecified and thus implementation-dependent (see :ref:`complex-number-ordering`).
 
 In-place Operators
 ~~~~~~~~~~~~~~~~~~