diff --git a/src/complex/Complex.js b/src/complex/Complex.js
index d934fd1..541d114 100644
--- a/src/complex/Complex.js
+++ b/src/complex/Complex.js
@@ -1,4 +1,4 @@
-import {Type} from '#core/Type.js'
+import {Returns, Type} from '#core/Type.js'
 import {match} from '#core/helpers.js'
 
 const isComplex = z => z && typeof z === 'object' && 're' in z && 'im' in z
@@ -66,6 +66,12 @@ function complexSpecialize(ComponentType) {
 export const Complex = new Type(isComplex, {
    specialize: complexSpecialize,
    specializesTo,
+   from: [match( // can promote any non-complex type T to Complex(T) as needed
+      // but watch out, this should be tried late, because it can preclude
+      // other more reasonable conversions like bool => number.
+      T => !T.complex,
+      (math, T) => Returns(Complex(T), r => math.complex(r, math.zero(T)))
+   )],
    refine: function(z, typer) {
       const reType = typer(z.re)
       const imType = typer(z.im)
diff --git a/src/complex/__test__/arithmetic.spec.js b/src/complex/__test__/arithmetic.spec.js
new file mode 100644
index 0000000..02dd56b
--- /dev/null
+++ b/src/complex/__test__/arithmetic.spec.js
@@ -0,0 +1,26 @@
+import assert from 'assert'
+import math from '#nanomath'
+
+const cplx = math.complex
+
+describe('complex arithmetic operations', () => {
+   it('computes absquare of complex numbers', () => {
+      assert.strictEqual(math.absquare(cplx(3, 4)), 25)
+      assert.strictEqual(math.absquare(cplx(cplx(2, 3), cplx(4,5))), 54)
+      assert.strictEqual(math.absquare(cplx(true, true)), 2)
+   })
+   it('adds complex numbers', () => {
+      const z = cplx(3, 4)
+      assert.deepStrictEqual(math.add(z, cplx(-1, 1)), cplx(2, 5))
+      assert.deepStrictEqual(math.add(z, cplx(true, false)), cplx(4, 4))
+      assert.deepStrictEqual(math.add(cplx(false, true), z), cplx(3, 5))
+      assert.deepStrictEqual(
+         math.add(cplx(z, z), cplx(cplx(0.5, 0.5), z)),
+         cplx(cplx(3.5, 4.5), cplx(6, 8)))
+      assert.deepStrictEqual(math.add(z, 5), cplx(8, 4))
+      assert.deepStrictEqual(math.add(true, z), cplx(4, 4))
+      assert.deepStrictEqual(math.add(cplx(z,z), 10), cplx(cplx(13, 4), z))
+      assert.deepStrictEqual(
+         math.add(cplx(z,z), cplx(10,20)), cplx(cplx(13, 4), cplx(23, 4)))
+   })
+})
diff --git a/src/complex/__test__/complex.spec.js b/src/complex/__test__/type.spec.js
similarity index 100%
rename from src/complex/__test__/complex.spec.js
rename to src/complex/__test__/type.spec.js
diff --git a/src/complex/all.js b/src/complex/all.js
index 9795516..5c261d4 100644
--- a/src/complex/all.js
+++ b/src/complex/all.js
@@ -1,2 +1,3 @@
 export * as typeDefinition from './Complex.js'
+export * as arithmetic from './arithmetic.js'
 export * as type from './type.js'
diff --git a/src/complex/arithmetic.js b/src/complex/arithmetic.js
new file mode 100644
index 0000000..0cef720
--- /dev/null
+++ b/src/complex/arithmetic.js
@@ -0,0 +1,17 @@
+import {Complex} from './Complex.js'
+import {match} from '#core/helpers.js'
+import {ReturnsAs} from '#generic/helpers.js'
+
+export const absquare = match(Complex, (math, C) => {
+    const compAbsq = math.absquare.resolve([C.Component])
+    const R = compAbsq.returns
+    const add = math.add.resolve([R,R])
+    return ReturnsAs(add, z => add(compAbsq(z.re), compAbsq(z.im)))
+})
+
+export const add = match([Complex, Complex], (math, [C, D]) => {
+    const addComps = math.add.resolve([C.Component, D.Component])
+    const cplx = math.complex.resolve([addComps.returns, addComps.returns])
+    return ReturnsAs(
+        cplx, (w,z) => cplx(addComps(w.re, z.re), addComps(w.im, z.im)))
+})
diff --git a/src/core/TypeDispatcher.js b/src/core/TypeDispatcher.js
index 202afe1..121d182 100644
--- a/src/core/TypeDispatcher.js
+++ b/src/core/TypeDispatcher.js
@@ -334,7 +334,7 @@ export class TypeDispatcher {
             try {
                theBehavior = item(
                   DependencyRecorder(this, '', this, []),
-                  matched(template))
+                  matched(template, this))
             } catch (e) {
                e.message = `Error in factory for ${key} on ${types} `
                   + `(match data ${template}): ${e.message}`
diff --git a/src/core/TypePatterns.js b/src/core/TypePatterns.js
index eb73afd..7c3e8cd 100644
--- a/src/core/TypePatterns.js
+++ b/src/core/TypePatterns.js
@@ -1,4 +1,5 @@
 import {Type, Undefined} from './Type.js'
+import {isPlainFunction} from './helpers.js'
 
 export class TypePattern {
    match(typeSequence, options={}) {
@@ -64,12 +65,34 @@ class SequencePattern extends TypePattern {
    }
 }
 
+class PredicatePattern extends TypePattern {
+   constructor(predicate) {
+      super()
+      this.predicate = predicate
+   }
+   match(typeSequence, options={}) {
+      const position = options.position ?? 0
+      const actual = typeSequence[position]
+      if (this.predicate(actual)) return [position + 1, actual]
+      return [-1, Undefined]
+   }
+   sampleTypes() {
+      throw new Error('sampleTypes() not yet implemented for PredicatePattern')
+   }
+   equal(other) {
+      return super.equal(other) && this.predicate === other.predicate
+   }
+}
+
 export const pattern = patternOrSpec => {
    if (patternOrSpec instanceof TypePattern) return patternOrSpec
    if (patternOrSpec instanceof Type) {
       return new MatchTypePattern(patternOrSpec)
    }
    if (Array.isArray(patternOrSpec)) return new SequencePattern(patternOrSpec)
+   if (isPlainFunction(patternOrSpec)) {
+      return new PredicatePattern(patternOrSpec)
+   }
    throw new TypeError(`Can't interpret '${patternOrSpec}' as a type pattern`)
 }
 
@@ -150,9 +173,16 @@ class PassthruPattern extends TypePattern {
 export const Passthru = new PassthruPattern()
 
 // returns the template just of matched types, dropping any actual types
-export const matched = (template) => {
-   if (Array.isArray(template)) return template.map(matched)
-   return template.matched ?? template
+export const matched = (template, math) => {
+   if (Array.isArray(template)) {
+      return template.map(pattern => matched(pattern, math))
+   }
+   if (template.matched) {
+      let convert = template.convertor
+      if (!convert.returns) convert = convert(math, template.actual)
+      return convert.returns || template.matched
+   }
+   return template
 }
 
 // checks if the template is just pass-through or needs collection
diff --git a/src/generic/relational.js b/src/generic/relational.js
index 810c06a..902835d 100644
--- a/src/generic/relational.js
+++ b/src/generic/relational.js
@@ -18,7 +18,7 @@ export const equal = match([Any, Any], (math, [T, U]) => {
       return boolnum(() => false)(math)
    }
    // Get the type of the first argument to the matching checker:
-   const ByType = matched(exactChecker.template).flat()[0]
+   const ByType = matched(exactChecker.template, math).flat()[0]
    // Now see if there are tolerances for that type:
    const typeConfig = math.resolve('config', [ByType])
    if ('relTol' in typeConfig) {
diff --git a/src/nanomath.js b/src/nanomath.js
index c133cbf..3038472 100644
--- a/src/nanomath.js
+++ b/src/nanomath.js
@@ -5,6 +5,14 @@ import * as numbers from './number/all.js'
 import * as complex from './complex/all.js'
 import {TypeDispatcher} from '#core/TypeDispatcher.js'
 
-const math = new TypeDispatcher(booleans, coretypes, generics, numbers, complex)
+// At the moment, since we are not sorting patterns in any way,
+// order matters in the construction. Patterns that come later in
+// the following list will be tried earlier. (The rationale for that
+// ordering is that any time you merge something, it should supersede
+// whatever has been merged before.)
+// Hence, in building the math instance, we put complex first because
+// we want its conversion (which converts _any_ non-complex type to
+// complex, potentially making a poor overload choice) to be tried last.
+const math = new TypeDispatcher(complex, generics, booleans, coretypes, numbers)
 
 export default math