diff --git a/src/cmd/compile/internal/gc/const.go b/src/cmd/compile/internal/gc/const.go
index f9ea92ce50..a465d4a7bb 100644
--- a/src/cmd/compile/internal/gc/const.go
+++ b/src/cmd/compile/internal/gc/const.go
@@ -1037,15 +1037,13 @@ func evconst(n *Node) {
 		cmplxmpy(v.U.(*Mpcplx), rv.U.(*Mpcplx))
 
 	case ODIV_ | CTCPLX_:
-		if rv.U.(*Mpcplx).Real.CmpFloat64(0) == 0 && rv.U.(*Mpcplx).Imag.CmpFloat64(0) == 0 {
+		if !cmplxdiv(v.U.(*Mpcplx), rv.U.(*Mpcplx)) {
 			yyerror("complex division by zero")
 			rv.U.(*Mpcplx).Real.SetFloat64(1.0)
 			rv.U.(*Mpcplx).Imag.SetFloat64(0.0)
 			break
 		}
 
-		cmplxdiv(v.U.(*Mpcplx), rv.U.(*Mpcplx))
-
 	case OEQ_ | CTNIL_:
 		goto settrue
 
@@ -1591,7 +1589,11 @@ func cmplxmpy(v *Mpcplx, rv *Mpcplx) {
 
 // complex divide v /= rv
 //	(a, b) / (c, d) = ((a*c + b*d), (b*c - a*d))/(c*c + d*d)
-func cmplxdiv(v *Mpcplx, rv *Mpcplx) {
+func cmplxdiv(v *Mpcplx, rv *Mpcplx) bool {
+	if rv.Real.CmpFloat64(0) == 0 && rv.Imag.CmpFloat64(0) == 0 {
+		return false
+	}
+
 	var ac Mpflt
 	var bd Mpflt
 	var bc Mpflt
@@ -1599,6 +1601,7 @@ func cmplxdiv(v *Mpcplx, rv *Mpcplx) {
 	var cc_plus_dd Mpflt
 
 	cc_plus_dd.Set(&rv.Real)
+
 	cc_plus_dd.Mul(&rv.Real) // cc
 
 	ac.Set(&rv.Imag)
@@ -1607,6 +1610,14 @@ func cmplxdiv(v *Mpcplx, rv *Mpcplx) {
 
 	cc_plus_dd.Add(&ac) // cc+dd
 
+	// We already checked that c and d are not both zero, but we can't
+	// assume that c²+d² != 0 follows, because for tiny values of c
+	// and/or d c²+d² can underflow to zero.  Check that c²+d² is
+	// nonzero,return if it's not.
+	if cc_plus_dd.CmpFloat64(0) == 0 {
+		return false
+	}
+
 	ac.Set(&v.Real)
 
 	ac.Mul(&rv.Real) // ac
@@ -1632,6 +1643,8 @@ func cmplxdiv(v *Mpcplx, rv *Mpcplx) {
 
 	v.Imag.Sub(&ad)         // bc-ad
 	v.Imag.Quo(&cc_plus_dd) // (bc+ad)/(cc+dd)
+
+	return true
 }
 
 // Is n a Go language constant (as opposed to a compile-time constant)?
diff --git a/src/go/types/stdlib_test.go b/src/go/types/stdlib_test.go
index a268d3b3bb..3f02dd98ba 100644
--- a/src/go/types/stdlib_test.go
+++ b/src/go/types/stdlib_test.go
@@ -171,6 +171,7 @@ func TestStdFixed(t *testing.T) {
 		"issue18459.go", // go/types doesn't check validity of //go:xxx directives
 		"issue18882.go", // go/types doesn't check validity of //go:xxx directives
 		"issue20232.go", // go/types handles larger constants than gc
+		"issue20227.go", // go/types does not handle this yet
 	)
 }
 
diff --git a/test/fixedbugs/issue20227.go b/test/fixedbugs/issue20227.go
new file mode 100644
index 0000000000..4448eb5438
--- /dev/null
+++ b/test/fixedbugs/issue20227.go
@@ -0,0 +1,16 @@
+// errorcheck
+
+// Copyright 2017 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Issue 20227: panic while constructing constant "1i/1e-600000000"
+
+package p
+
+var _ = 1 / 1e-600000000i  // ERROR "complex division by zero"
+var _ = 1i / 1e-600000000  // ERROR "complex division by zero"
+var _ = 1i / 1e-600000000i // ERROR "complex division by zero"
+
+var _ = 1 / (1e-600000000 + 1e-600000000i)  // ERROR "complex division by zero"
+var _ = 1i / (1e-600000000 + 1e-600000000i) // ERROR "complex division by zero"