diff --git a/Lib/test/test_complex.py b/Lib/test/test_complex.py
index 56e9083..60c5252 100644
--- a/Lib/test/test_complex.py
+++ b/Lib/test/test_complex.py
@@ -431,6 +431,13 @@
 
     @unittest.skipUnless(float.__getformat__("double").startswith("IEEE"),
                          "test requires IEEE 754 doubles")
+    def test_overflow(self):
+        self.assertEqual(complex("1e500"), complex(INF, 0.0))
+        self.assertEqual(complex("-1e500j"), complex(0.0, -INF))
+        self.assertEqual(complex("-1e500+1.8e308j"), complex(-INF, INF))
+
+    @unittest.skipUnless(float.__getformat__("double").startswith("IEEE"),
+                         "test requires IEEE 754 doubles")
     def test_repr_roundtrip(self):
         vals = [0.0, 1e-500, 1e-315, 1e-200, 0.0123, 3.1415, 1e50, INF, NAN]
         vals += [-v for v in vals]
diff --git a/Misc/NEWS b/Misc/NEWS
index 6051d1b..db2d60d 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -12,6 +12,10 @@
 Core and Builtins
 -----------------
 
+- Issue #5829: complex("1e500") no longer raises OverflowError.  This
+  makes it consistent with float("1e500") and interpretation of real
+  and imaginary literals.
+
 - Issue #3527: Removed Py_WIN_WIDE_FILENAMES which is not used any more.
 
 - __instancecheck__ and __subclasscheck__ are now completely ignored on classic
diff --git a/Objects/complexobject.c b/Objects/complexobject.c
index 6e31723..b976b6d 100644
--- a/Objects/complexobject.c
+++ b/Objects/complexobject.c
@@ -989,8 +989,6 @@
 	z = PyOS_ascii_strtod(s, &end);
 	if (end == s && errno == ENOMEM)
 		return PyErr_NoMemory();
-	if (errno == ERANGE && fabs(z) >= 1.0)
-		goto overflow;
 
 	if (end != s) {
 		/* all 4 forms starting with <float> land here */
@@ -1002,8 +1000,6 @@
 			y = PyOS_ascii_strtod(s, &end);
 			if (end == s && errno == ENOMEM)
 				return PyErr_NoMemory();
-			if (errno == ERANGE && fabs(y) >= 1.0)
-				goto overflow;
 			if (end != s)
 				/* <float><signed-float>j */
 				s = end;
@@ -1063,11 +1059,6 @@
 	PyErr_SetString(PyExc_ValueError,
 			"complex() arg is a malformed string");
 	return NULL;
-
-  overflow:
-	PyErr_SetString(PyExc_OverflowError,
-			"complex() arg overflow");
-	return NULL;
 }
 
 static PyObject *