Document breaking change: Complex special-value results now follow C23 Annex G

docs/core/compatibility/11.md

@@ -23,6 +23,7 @@ See [Breaking changes in ASP.NET Core 11](/aspnet/core/breaking-changes/11/overv
 | Title                                                             | Type of change    |
 |-------------------------------------------------------------------|-------------------|
 | [CborReader and CborWriter enforce a default maximum nesting depth](core-libraries/11/cbor-max-depth.md) | Behavioral change |
+| [Complex special-value results now follow C23 Annex G](core-libraries/11/complex-annex-g-special-values.md) | Behavioral change |
 | [CRC32 validation added when reading ZIP archive entries](core-libraries/11/ziparchive-entry-crc32-validation.md) | Behavioral change |
 | [DateOnly and TimeOnly TryParse methods throw for invalid input](core-libraries/11/dateonly-timeonly-tryparse-argumentexception.md) | Behavioral change |
 | [DeflateStream and GZipStream write headers and footers for empty payload](core-libraries/11/deflatestream-gzipstream-empty-payload.md) | Behavioral change |

docs/core/compatibility/core-libraries/11/complex-annex-g-special-values.md

@@ -0,0 +1,77 @@
+---
+title: "Breaking change: System.Numerics.Complex special-value results now follow C23 Annex G"
+description: "Learn about the breaking change in .NET 11 where System.Numerics.Complex arithmetic and math functions return C23 Annex G-conformant special values for signed zeros, infinities, and NaNs."
+ms.date: 08/04/2026
+ai-usage: ai-assisted
+---
+
+# System.Numerics.Complex special-value results now follow C23 Annex G
+
+<xref:System.Numerics.Complex> arithmetic operators and math functions now produce the special-value results (for signed zeros, infinities, and NaNs) required by C23 Annex G (IEC 60559-compatible complex arithmetic). Because `Complex` now delegates most of its implementation to the new `Complex<double>` type, the conformant special-value handling flows through to it.
+
+## Version introduced
+
+.NET 11 Preview 7
+
+## Previous behavior
+
+Previously, for non-finite (and some overflowing) inputs, `Complex` arithmetic and elementary functions frequently returned `(NaN, NaN)` even when a directed infinity or signed result was mathematically appropriate.
+
+```csharp
+using System.Numerics;
+
+Complex.Atan(new Complex(double.PositiveInfinity, 1.0)); // (NaN, NaN)
+Complex.Acos(new Complex(double.NegativeInfinity, double.NaN)); // (NaN, NaN)
+Complex.Cosh(new Complex(double.PositiveInfinity, double.PositiveInfinity)); // (NaN, NaN)
+
+// An infinite operand could collapse the product to NaN:
+new Complex(double.PositiveInfinity, double.PositiveInfinity) * new Complex(1.0, 0.0); // (NaN, NaN)
+```
+
+## New behavior
+
+Starting in .NET 11, the same inputs return the C23 Annex G special values.
+
+```csharp
+using System.Numerics;
+
+Complex.Atan(new Complex(double.PositiveInfinity, 1.0)); // (π/2, 0)
+Complex.Acos(new Complex(double.NegativeInfinity, double.NaN)); // (NaN, +∞)
+Complex.Cosh(new Complex(double.PositiveInfinity, double.PositiveInfinity)); // (+∞, NaN)
+
+// An infinite operand now yields a directed infinity (Annex G.5.1 recovery):
+new Complex(double.PositiveInfinity, double.PositiveInfinity) * new Complex(1.0, 0.0); // (+∞, +∞)
+```
+
+Division by a zero divisor is likewise governed by Annex G: the result is a directed infinity, or NaN for `0/0`. For example, `(1, 0) / (0, 0)` yields an infinite real component rather than a fully NaN result.
+
+The change spans `operator *`, `operator /`, `Multiply`, `Divide`, `Reciprocal`, `Abs`, `Pow`, and the elementary functions (`Sqrt`, `Exp`, `Log`, `Log10`, and the trigonometric, hyperbolic, and inverse-trigonometric functions). One case Annex G leaves explicitly unspecified—the sign of a zero-valued quotient component from `operator /`—might also differ.
+
+## Type of breaking change
+
+This change is a [behavioral change](../../categories.md#behavioral-change).
+
+## Reason for change
+
+Complex numbers are outside the scope of IEEE 754 itself, so C23 Annex G is the relevant specification of the special-value behavior IEEE 754 otherwise implies for the scalar operations complex arithmetic is built on. The previous implementation returned `NaN` for many inputs where Annex G requires a directed infinity or a signed result, which is both non-conformant and less useful for downstream numerical code, because it lost the sign or direction information that an infinite intermediate value carries. The new generic `Complex<T>` type was made conformant, and the shipped `Complex` type inherits that conformance by delegation.
+
+For more information, see [dotnet/runtime#131132](https://github.com/dotnet/runtime/pull/131132).
+
+## Recommended action
+
+Most code benefits from the more accurate results and needs no change. If your code explicitly depends on the previous `(NaN, NaN)` results for special-value inputs—for example, tests that assert `NaN` for `Complex` operations on infinities, or logic that treats any non-finite input as producing `NaN`—update it to expect the Annex G values. There's no compatibility switch to restore the previous behavior.
+
+## Affected APIs
+
+- <xref:System.Numerics.Complex.op_Multiply(System.Numerics.Complex,System.Numerics.Complex)>
+- <xref:System.Numerics.Complex.op_Division(System.Numerics.Complex,System.Numerics.Complex)>
+- <xref:System.Numerics.Complex.Multiply(System.Numerics.Complex,System.Numerics.Complex)>
+- <xref:System.Numerics.Complex.Divide(System.Numerics.Complex,System.Numerics.Complex)>
+- <xref:System.Numerics.Complex.Reciprocal(System.Numerics.Complex)>
+- <xref:System.Numerics.Complex.Abs(System.Numerics.Complex)>
+- <xref:System.Numerics.Complex.Pow(System.Numerics.Complex,System.Numerics.Complex)> and <xref:System.Numerics.Complex.Pow(System.Numerics.Complex,System.Double)>
+- <xref:System.Numerics.Complex.Sqrt(System.Numerics.Complex)>
+- <xref:System.Numerics.Complex.Exp(System.Numerics.Complex)>
+- <xref:System.Numerics.Complex.Log(System.Numerics.Complex)> (all overloads) and <xref:System.Numerics.Complex.Log10(System.Numerics.Complex)>
+- <xref:System.Numerics.Complex.Sin(System.Numerics.Complex)>, <xref:System.Numerics.Complex.Cos(System.Numerics.Complex)>, <xref:System.Numerics.Complex.Tan(System.Numerics.Complex)>, <xref:System.Numerics.Complex.Sinh(System.Numerics.Complex)>, <xref:System.Numerics.Complex.Cosh(System.Numerics.Complex)>, <xref:System.Numerics.Complex.Tanh(System.Numerics.Complex)>
+- <xref:System.Numerics.Complex.Asin(System.Numerics.Complex)>, <xref:System.Numerics.Complex.Acos(System.Numerics.Complex)>, <xref:System.Numerics.Complex.Atan(System.Numerics.Complex)>

docs/core/compatibility/toc.yml

@@ -12,6 +12,8 @@ items:
             items:
               - name: CborReader and CborWriter enforce a default maximum nesting depth
                 href: core-libraries/11/cbor-max-depth.md
+              - name: Complex special-value results now follow C23 Annex G
+                href: core-libraries/11/complex-annex-g-special-values.md
               - name: CRC32 validation added when reading ZIP archive entries
                 href: core-libraries/11/ziparchive-entry-crc32-validation.md
               - name: DateOnly and TimeOnly TryParse methods throw for invalid input