added complext number support

docs/Complex.md

@@ -0,0 +1,82 @@
+# Complex Numbers (`lyng.complex`)
+
+`lyng.complex` adds a pure-Lyng `Complex` type backed by `Real` components.
+
+Import it when you want ordinary complex arithmetic:
+
+```lyng
+import lyng.complex
+```
+
+## Construction
+
+Use any of these:
+
+```lyng
+import lyng.complex
+
+val a = Complex(1.0, 2.0)
+val b = complex(1.0, 2.0)
+val c = 2.i
+val d = 3.re
+
+assertEquals(Complex(1.0, 2.0), 1 + 2.i)
+```
+
+Convenience extensions:
+
+- `Int.re`, `Real.re`: embed a real value into the complex plane
+- `Int.i`, `Real.i`: create a pure imaginary value
+- `cis(angle)`: shorthand for `cos(angle) + i sin(angle)`
+
+## Core Operations
+
+`Complex` supports:
+
+- `+`
+- `-`
+- `*`
+- `/`
+- unary `-`
+- `conjugate`
+- `magnitude`
+- `phase`
+
+Mixed arithmetic with `Int` and `Real` is enabled through `lyng.operators`, so both sides work naturally:
+
+```lyng
+import lyng.complex
+
+assertEquals(Complex(1.0, 2.0), 1 + 2.i)
+assertEquals(Complex(1.5, 2.0), 1.5 + 2.i)
+assertEquals(Complex(2.0, 2.0), 2.i + 2)
+```
+
+Mixed equality with built-in numeric types is intentionally not promised yet. Keep equality checks in the `Complex` domain for now.
+
+## Transcendental Functions
+
+For now, use member-style calls:
+
+```lyng
+import lyng.complex
+
+val z = 1 + π.i
+val w = z.exp()
+val s = z.sin()
+val r = z.sqrt()
+```
+
+This is deliberate. Lyng already has built-in top-level real-valued functions such as `exp(x)` and `sin(x)`, and imported modules do not currently replace those root bindings. So plain `exp(z)` is not yet the right extension mechanism for complex math.
+
+## Design Scope
+
+This module intentionally uses `Complex` with `Real` parts, not `Complex<T>`.
+
+Reasons:
+
+- the existing math runtime is `Real`-centric
+- the operator interop registry works with concrete runtime classes
+- transcendental functions (`exp`, `sin`, `ln`, `sqrt`) are defined over the `Real` math backend here
+
+If Lyng later gets a more general numeric-trait or callable-overload registry, a generic algebraic `Complex<T>` can be revisited on firmer ground.

docs/ai_stdlib_reference.md

@@ -56,6 +56,8 @@ Sources: `lynglib/src/commonMain/kotlin/net/sergeych/lyng/Script.kt`, `lynglib/s
 ## 5. Additional Built-in Modules (import explicitly)
 - `import lyng.observable`
   - `Observable`, `Subscription`, `ObservableList`, `ListChange` and change subtypes, `ChangeRejectionException`.
+- `import lyng.complex`
+  - `Complex`, `complex(re, im)`, `cis(angle)`, and numeric embedding extensions such as `2.i` / `3.re`.
 - `import lyng.buffer`
   - `Buffer`, `MutableBuffer`.
 - `import lyng.serialization`