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
@@ -351,6 +351,8 @@
     %a = complex.mul %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
@@ -248,6 +248,29 @@
   return {};
 }
 
+//===----------------------------------------------------------------------===//
+// MulOp
+//===----------------------------------------------------------------------===//
+
+OpFoldResult MulOp::fold(FoldAdaptor adaptor) {
+  auto constant = getRhs().getDefiningOp<ConstantOp>();
+  if (!constant)
+    return {};
+
+  ArrayAttr arrayAttr = constant.getValue();
+  APFloat real = cast<FloatAttr>(arrayAttr[0]).getValue();
+  APFloat imag = cast<FloatAttr>(arrayAttr[1]).getValue();
+
+  if (!imag.isZero())
+    return {};
+
+  // complex.mul(a, complex.constant<1.0, 0.0>) -> a
+  if (real == APFloat(real.getSemantics(), 1))
+    return 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
@@ -177,3 +177,58 @@
   // CHECK-NEXT: return %[[NEG]]
   return %im : f32
 }
+
+// CHECK-LABEL: func @mul_one_f16
+//  CHECK-SAME: (%[[ARG0:.*]]: f16, %[[ARG1:.*]]: f16) -> complex<f16>
+func.func @mul_one_f16(%arg0: f16, %arg1: f16) -> complex<f16> {
+  %create = complex.create %arg0, %arg1: complex<f16>  
+  %one = complex.constant [1.0 : f16, 0.0 : f16] : complex<f16>
+  %mul = complex.mul %create, %one : complex<f16>
+  // CHECK: %[[CREATE:.*]] = complex.create %[[ARG0]], %[[ARG1]] : complex<f16>
+  // CHECK-NEXT: return %[[CREATE]]
+  return %mul : complex<f16>
+}
+
+// CHECK-LABEL: func @mul_one_f32
+//  CHECK-SAME: (%[[ARG0:.*]]: f32, %[[ARG1:.*]]: f32) -> complex<f32>
+func.func @mul_one_f32(%arg0: f32, %arg1: f32) -> complex<f32> {
+  %create = complex.create %arg0, %arg1: complex<f32>  
+  %one = complex.constant [1.0 : f32, 0.0 : f32] : complex<f32>
+  %mul = complex.mul %create, %one : complex<f32>
+  // CHECK: %[[CREATE:.*]] = complex.create %[[ARG0]], %[[ARG1]] : complex<f32>
+  // CHECK-NEXT: return %[[CREATE]]
+  return %mul : complex<f32>
+}
+
+// CHECK-LABEL: func @mul_one_f64
+//  CHECK-SAME: (%[[ARG0:.*]]: f64, %[[ARG1:.*]]: f64) -> complex<f64>
+func.func @mul_one_f64(%arg0: f64, %arg1: f64) -> complex<f64> {
+  %create = complex.create %arg0, %arg1: complex<f64>  
+  %one = complex.constant [1.0 : f64, 0.0 : f64] : complex<f64>
+  %mul = complex.mul %create, %one : complex<f64>
+  // CHECK: %[[CREATE:.*]] = complex.create %[[ARG0]], %[[ARG1]] : complex<f64>
+  // CHECK-NEXT: return %[[CREATE]]
+  return %mul : complex<f64>
+}
+
+// CHECK-LABEL: func @mul_one_f80
+//  CHECK-SAME: (%[[ARG0:.*]]: f80, %[[ARG1:.*]]: f80) -> complex<f80>
+func.func @mul_one_f80(%arg0: f80, %arg1: f80) -> complex<f80> {
+  %create = complex.create %arg0, %arg1: complex<f80>  
+  %one = complex.constant [1.0 : f80, 0.0 : f80] : complex<f80>
+  %mul = complex.mul %create, %one : complex<f80>
+  // CHECK: %[[CREATE:.*]] = complex.create %[[ARG0]], %[[ARG1]] : complex<f80>
+  // CHECK-NEXT: return %[[CREATE]]
+  return %mul : complex<f80>
+}
+
+// CHECK-LABEL: func @mul_one_f128
+//  CHECK-SAME: (%[[ARG0:.*]]: f128, %[[ARG1:.*]]: f128) -> complex<f128>
+func.func @mul_one_f128(%arg0: f128, %arg1: f128) -> complex<f128> {
+  %create = complex.create %arg0, %arg1: complex<f128>  
+  %one = complex.constant [1.0 : f128, 0.0 : f128] : complex<f128>
+  %mul = complex.mul %create, %one : complex<f128>
+  // CHECK: %[[CREATE:.*]] = complex.create %[[ARG0]], %[[ARG1]] : complex<f128>
+  // CHECK-NEXT: return %[[CREATE]]
+  return %mul : complex<f128>
+}