Index: Python/pystrtod.c
===================================================================
--- Python/pystrtod.c	(revision 71809)
+++ Python/pystrtod.c	(working copy)
@@ -733,6 +733,10 @@
 		   so convert Infinity to inf and NaN to nan, and
 		   ignore sign of nan. Then return. */
 
+		/* ignore the actual sign of a nan */
+		if (digits[0] == 'n' || digits[0] == 'N')
+			sign = 0;
+
 		/* We only need 5 bytes to hold the result "+inf\0" . */
 		bufsize = 5; /* Used later in an assert. */
 		buf = (char *)PyMem_Malloc(bufsize);
@@ -742,13 +746,13 @@
 		}
 		p = buf;
 
+		if (sign == 1) {
+			*p++ = '-';
+		}
+		else if (always_add_sign) {
+			*p++ = '+';
+		}
 		if (digits[0] == 'i' || digits[0] == 'I') {
-			if (sign == 1) {
-				*p++ = '-';
-			}
-			else if (always_add_sign) {
-				*p++ = '+';
-			}
 			strncpy(p, float_strings[OFS_INF], 3);
 			p += 3;
 
@@ -756,8 +760,6 @@
 				*type = Py_DTST_INFINITE;
 		}
 		else if (digits[0] == 'n' || digits[0] == 'N') {
-			/* note that we *never* add a sign for a nan,
-			   even if one has explicitly been requested */
 			strncpy(p, float_strings[OFS_NAN], 3);
 			p += 3;
 
Index: Objects/complexobject.c
===================================================================
--- Objects/complexobject.c	(revision 71809)
+++ Objects/complexobject.c	(working copy)
@@ -347,65 +347,32 @@
     char *lead = "";
     char *tail = "";
 
-
-    if (v->cval.real == 0.) {
+    if (v->cval.real == 0. && copysign(1.0, v->cval.real)==1.0) {
         re = "";
-        if (!Py_IS_FINITE(v->cval.imag)) {
-            if (Py_IS_NAN(v->cval.imag))
-                im = "nan*";
-            else if (copysign(1, v->cval.imag) == 1)
-                im = "inf*";
-            else
-                im = "-inf*";
+        pim = PyOS_double_to_string(v->cval.imag, format_code,
+                                    0, 0, NULL);
+        if (!pim) {
+            PyErr_NoMemory();
+            goto done;
         }
-        else {
-            pim = PyOS_double_to_string(v->cval.imag, format_code,
-                                        0, 0, NULL);
-            if (!pim) {
-                PyErr_NoMemory();
-                goto done;
-            }
-            im = pim;
-        }
+        im = pim;
     } else {
         /* Format imaginary part with sign, real part without */
-        if (!Py_IS_FINITE(v->cval.real)) {
-            if (Py_IS_NAN(v->cval.real))
-                re = "nan";
-            /* else if (copysign(1, v->cval.real) == 1) */
-            else if (v->cval.real > 0)
-                re = "inf";
-            else
-                re = "-inf";
-        }
-        else {
-            pre = PyOS_double_to_string(v->cval.real, format_code,
+        pre = PyOS_double_to_string(v->cval.real, format_code,
                                         0, 0, NULL);
-            if (!pre) {
-                PyErr_NoMemory();
-                goto done;
-            }
-            re = pre;
+        if (!pre) {
+            PyErr_NoMemory();
+            goto done;
         }
+        re = pre;
 
-        if (!Py_IS_FINITE(v->cval.imag)) {
-            if (Py_IS_NAN(v->cval.imag))
-                im = "+nan*";
-            /* else if (copysign(1, v->cval.imag) == 1) */
-            else if (v->cval.imag > 0)
-                im = "+inf*";
-            else
-                im = "-inf*";
-        }
-        else {
-            pim = PyOS_double_to_string(v->cval.imag, format_code,
+        pim = PyOS_double_to_string(v->cval.imag, format_code,
                                         0, Py_DTSF_SIGN, NULL);
-            if (!pim) {
-                PyErr_NoMemory();
-                goto done;
-            }
-            im = pim;
+        if (!pim) {
+            PyErr_NoMemory();
+            goto done;
         }
+        im = pim;
         lead = "(";
         tail = ")";
     }
@@ -756,12 +723,8 @@
 {
 	const char *s, *start;
 	char *end;
-	double x=0.0, y=0.0, z;
-	int got_re=0, got_im=0, got_bracket=0, done=0;
-	int digit_or_dot;
-	int sw_error=0;
-	int sign;
-	char buffer[256]; /* For errors */
+	double x, y;
+	int got_bracket=0;
 	char s_buffer[256];
 	Py_ssize_t len;
 
@@ -785,16 +748,13 @@
 		return NULL;
 	}
 
+	errno = 0;
+
 	/* position on first nonblank */
 	start = s;
 	while (*s && isspace(Py_CHARMASK(*s)))
 		s++;
-	if (s[0] == '\0') {
-		PyErr_SetString(PyExc_ValueError,
-				"complex() arg is an empty string");
-		return NULL;
-	}
-	if (s[0] == '(') {
+	if (*s == '(') {
 		/* Skip over possible bracket from repr(). */
 		got_bracket = 1;
 		s++;
@@ -802,120 +762,51 @@
 			s++;
 	}
 
-	z = -1.0;
-	sign = 1;
-	do {
+	/* get float */
+	x = PyOS_ascii_strtod(s, &end);
+	if (end == s)
+		goto error;
+	s = end;
+	if (*s == '+' || *s == '-') {
+		/* we've got a real part *and* an imaginary part */
+		y = PyOS_ascii_strtod(s, &end);
+		if (end == s || !(*end == 'j' || *end == 'J'))
+			goto error;
+		s = ++end;
+	}
+	else if (*s == 'j' || *s == 'J') {
+		/* no real part; x is the imaginary part; swap around */
+		s++;
+		y = x;
+		x = 0.0;
+	}
+	else
+		/* no imaginary part */
+		y = 0.0;
 
-		switch (*s) {
-
-		case '\0':
-			if (s-start != len) {
-				PyErr_SetString(
-					PyExc_ValueError,
-					"complex() arg contains a null byte");
-				return NULL;
-			}
-			if(!done) sw_error=1;
-			break;
-
-		case ')':
-			if (!got_bracket || !(got_re || got_im)) {
-				sw_error=1;
-				break;
-			}
-			got_bracket=0;
-			done=1;
-			s++;
-			while (*s && isspace(Py_CHARMASK(*s)))
-				s++;
-			if (*s) sw_error=1;
-			break;
-
-		case '-':
-			sign = -1;
-				/* Fallthrough */
-		case '+':
-			if (done)  sw_error=1;
-			s++;
-			if  (  *s=='\0'||*s=='+'||*s=='-'||*s==')'||
-			       isspace(Py_CHARMASK(*s))  )  sw_error=1;
-			break;
-
-		case 'J':
-		case 'j':
-			if (got_im || done) {
-				sw_error = 1;
-				break;
-			}
-			if  (z<0.0) {
-				y=sign;
-			}
-			else{
-				y=sign*z;
-			}
-			got_im=1;
-			s++;
-			if  (*s!='+' && *s!='-' )
-				done=1;
-			break;
-
-		default:
-			if (isspace(Py_CHARMASK(*s))) {
-				while (*s && isspace(Py_CHARMASK(*s)))
-					s++;
-				if (*s && *s != ')')
-					sw_error=1;
-				else
-					done = 1;
-				break;
-			}
-			digit_or_dot =
-				(*s=='.' || isdigit(Py_CHARMASK(*s)));
-			if  (done||!digit_or_dot) {
-				sw_error=1;
-				break;
-			}
-			errno = 0;
-			PyFPE_START_PROTECT("strtod", return 0)
-				z = PyOS_ascii_strtod(s, &end) ;
-			PyFPE_END_PROTECT(z)
-				if (errno != 0) {
-					PyOS_snprintf(buffer, sizeof(buffer),
-					  "float() out of range: %.150s", s);
-					PyErr_SetString(
-						PyExc_ValueError,
-						buffer);
-					return NULL;
-				}
-			s=end;
-			if  (*s=='J' || *s=='j') {
-
-				break;
-			}
-			if  (got_re) {
-				sw_error=1;
-				break;
-			}
-
-				/* accept a real part */
-			x=sign*z;
-			got_re=1;
-			if  (got_im)  done=1;
-			z = -1.0;
-			sign = 1;
-			break;
-
-		}  /* end of switch  */
-
-	} while (s - start < len && !sw_error);
-
-	if (sw_error || got_bracket) {
-		PyErr_SetString(PyExc_ValueError,
-				"complex() arg is a malformed string");
-		return NULL;
+	/* trailing whitespace and closing bracket */
+	while (*s && isspace(Py_CHARMASK(*s)))
+		s++;
+	if (got_bracket && *s == ')') {
+		got_bracket = 0;
+		s++;
+		while (*s && isspace(Py_CHARMASK(*s)))
+		       s++;
 	}
+	/* we should now be at the end of the string */
+	if (*s != '\0' || s-start != len || got_bracket)
+		goto error;
 
 	return complex_subtype_from_doubles(type, x, y);
+
+  error:
+	/* check for PyOS_ascii_strtod failure due to lack of memory */
+	if (errno == ENOMEM)
+		return PyErr_NoMemory();
+	PyErr_SetString(PyExc_ValueError,
+			"complex() arg is a malformed string");
+	return NULL;
+
 }
 
 static PyObject *
Index: Lib/test/test_complex.py
===================================================================
--- Lib/test/test_complex.py	(revision 71809)
+++ Lib/test/test_complex.py	(working copy)
@@ -202,6 +202,8 @@
         self.assertAlmostEqual(complex("+1"), +1)
         self.assertAlmostEqual(complex("(1+2j)"), 1+2j)
         self.assertAlmostEqual(complex("(1.3+2.2j)"), 1.3+2.2j)
+        self.assertAlmostEqual(complex("3.14+1J"), 3.14+1j)
+        self.assertAlmostEqual(complex(" ( +3.14-6J )"), 3.14-6j)
 
         class complex2(complex): pass
         self.assertAlmostEqual(complex(complex2(1+1j)), 1+1j)
@@ -229,8 +231,6 @@
         self.assertRaises(TypeError, complex, "1", "1")
         self.assertRaises(TypeError, complex, 1, "1")
 
-        self.assertEqual(complex("  3.14+J  "), 3.14+1j)
-
         # SF bug 543840:  complex(string) accepts strings with \0
         # Fixed in 2.3.
         self.assertRaises(ValueError, complex, '1+1j\0j')
@@ -254,6 +254,11 @@
         self.assertRaises(ValueError, complex, "(1+2j)123")
         self.assertRaises(ValueError, complex, "1"*500)
         self.assertRaises(ValueError, complex, "x")
+        self.assertRaises(ValueError, complex, "J")
+        self.assertRaises(ValueError, complex, "1j+2")
+        self.assertRaises(ValueError, complex, "1e1ej")
+        self.assertRaises(ValueError, complex, "1e++1ej")
+        self.assertRaises(ValueError, complex, ")1+2j(")
 
         class EvilExc(Exception):
             pass
@@ -318,17 +323,17 @@
         self.assertEqual(-6j,complex(repr(-6j)))
         self.assertEqual(6j,complex(repr(6j)))
 
-        self.assertEqual(repr(complex(1., INF)), "(1+inf*j)")
-        self.assertEqual(repr(complex(1., -INF)), "(1-inf*j)")
+        self.assertEqual(repr(complex(1., INF)), "(1+infj)")
+        self.assertEqual(repr(complex(1., -INF)), "(1-infj)")
         self.assertEqual(repr(complex(INF, 1)), "(inf+1j)")
-        self.assertEqual(repr(complex(-INF, INF)), "(-inf+inf*j)")
+        self.assertEqual(repr(complex(-INF, INF)), "(-inf+infj)")
         self.assertEqual(repr(complex(NAN, 1)), "(nan+1j)")
-        self.assertEqual(repr(complex(1, NAN)), "(1+nan*j)")
-        self.assertEqual(repr(complex(NAN, NAN)), "(nan+nan*j)")
+        self.assertEqual(repr(complex(1, NAN)), "(1+nanj)")
+        self.assertEqual(repr(complex(NAN, NAN)), "(nan+nanj)")
 
-        self.assertEqual(repr(complex(0, INF)), "inf*j")
-        self.assertEqual(repr(complex(0, -INF)), "-inf*j")
-        self.assertEqual(repr(complex(0, NAN)), "nan*j")
+        self.assertEqual(repr(complex(0, INF)), "infj")
+        self.assertEqual(repr(complex(0, -INF)), "-infj")
+        self.assertEqual(repr(complex(0, NAN)), "nanj")
 
     def test_neg(self):
         self.assertEqual(-(1+6j), -1-6j)