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
@@ -121,6 +121,15 @@
     if (getLhs() == sub.getRhs())
       return sub.getLhs();
 
+  // complex.add(a, complex.constant<0.0, 0.0>) -> a
+  if (auto constantOp = getRhs().getDefiningOp<ConstantOp>()) {
+    auto arrayAttr = constantOp.getValue();
+    if (arrayAttr[0].cast<FloatAttr>().getValue().isZero() &&
+        arrayAttr[1].cast<FloatAttr>().getValue().isZero()) {
+      return getLhs();
+    }
+  }
+
   return {};
 }
 
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
@@ -123,4 +123,14 @@
   %conj1 = complex.conj %complex1 : complex<f32>
   %conj2 = complex.conj %conj1 : complex<f32>
   return %conj2 : complex<f32>
+}
+
+// CHECK-LABEL: func @complex_add_zero
+func.func @complex_add_zero() -> complex<f32> {
+  %complex1 = complex.constant [1.0 : f32, 0.0 : f32] : complex<f32>
+  %complex2 = complex.constant [0.0 : f32, 0.0 : f32] : complex<f32>
+  // CHECK: %[[CPLX:.*]] = complex.constant [1.000000e+00 : f32, 0.000000e+00 : f32] : complex<f32>
+  // CHECK-NEXT: return %[[CPLX:.*]] : complex<f32>
+  %add = complex.add %complex1, %complex2 : complex<f32>
+  return %add : complex<f32>
 }
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