diff --git a/mlir/include/mlir/Dialect/Complex/IR/ComplexOps.td b/mlir/include/mlir/Dialect/Complex/IR/ComplexOps.td
--- a/mlir/include/mlir/Dialect/Complex/IR/ComplexOps.td
+++ b/mlir/include/mlir/Dialect/Complex/IR/ComplexOps.td
@@ -73,6 +73,8 @@
     %a = complex.add %b, %c : complex<f32>
     ```
   }];
+
+  let hasFolder = 1;
 }
 
 //===----------------------------------------------------------------------===//
diff --git a/mlir/lib/Dialect/Complex/IR/ComplexOps.cpp b/mlir/lib/Dialect/Complex/IR/ComplexOps.cpp
--- a/mlir/lib/Dialect/Complex/IR/ComplexOps.cpp
+++ b/mlir/lib/Dialect/Complex/IR/ComplexOps.cpp
@@ -8,6 +8,7 @@
 
 #include "mlir/Dialect/Complex/IR/Complex.h"
 #include "mlir/IR/Builders.h"
+#include "mlir/IR/Matchers.h"
 
 using namespace mlir;
 using namespace mlir::complex;
@@ -103,6 +104,26 @@
   return {};
 }
 
+//===----------------------------------------------------------------------===//
+// AddOp
+//===----------------------------------------------------------------------===//
+
+OpFoldResult AddOp::fold(ArrayRef<Attribute> operands) {
+  assert(operands.size() == 2 && "binary op takes 2 operands");
+
+  // complex.add(complex.sub(a, b), b) -> a
+  if (auto sub = getLhs().getDefiningOp<SubOp>())
+    if (getRhs() == sub.getRhs())
+      return sub.getLhs();
+
+  // complex.add(b, complex.sub(a, b)) -> a
+  if (auto sub = getRhs().getDefiningOp<SubOp>())
+    if (getLhs() == sub.getRhs())
+      return sub.getLhs();
+
+  return {};
+}
+
 //===----------------------------------------------------------------------===//
 // TableGen'd op method definitions
 //===----------------------------------------------------------------------===//
diff --git a/mlir/test/Dialect/Complex/canonicalize.mlir b/mlir/test/Dialect/Complex/canonicalize.mlir
--- a/mlir/test/Dialect/Complex/canonicalize.mlir
+++ b/mlir/test/Dialect/Complex/canonicalize.mlir
@@ -62,3 +62,25 @@
   %1 = complex.im %complex : complex<f32>
   return %1 : f32
 }
+
+// CHECK-LABEL: func @complex_add_sub_lhs
+func.func @complex_add_sub_lhs() -> complex<f32> {
+  %complex1 = complex.constant [1.0 : f32, 0.0 : f32] : complex<f32>
+  %complex2 = complex.constant [0.0 : f32, 2.0 : f32] : complex<f32>
+  // CHECK: %[[CPLX:.*]] = complex.constant [1.000000e+00 : f32, 0.000000e+00 : f32] : complex<f32>
+  // CHECK-NEXT: return %[[CPLX:.*]] : complex<f32>
+  %sub = complex.sub %complex1, %complex2 : complex<f32>
+  %add = complex.add %sub, %complex2 : complex<f32>
+  return %add : complex<f32>
+}
+
+// CHECK-LABEL: func @complex_add_sub_rhs
+func.func @complex_add_sub_rhs() -> complex<f32> {
+  %complex1 = complex.constant [1.0 : f32, 0.0 : f32] : complex<f32>
+  %complex2 = complex.constant [0.0 : f32, 2.0 : f32] : complex<f32>
+  // CHECK: %[[CPLX:.*]] = complex.constant [1.000000e+00 : f32, 0.000000e+00 : f32] : complex<f32>
+  // CHECK-NEXT: return %[[CPLX:.*]] : complex<f32>
+  %sub = complex.sub %complex1, %complex2 : complex<f32>
+  %add = complex.add %complex2, %sub : complex<f32>
+  return %add : complex<f32>
+}
\ No newline at end of file