diff --git a/src/c/_cffi_backend.c b/src/c/_cffi_backend.c
index 3f3a1aac..51850018 100644
--- a/src/c/_cffi_backend.c
+++ b/src/c/_cffi_backend.c
@@ -217,7 +217,7 @@
 #define CT_UNION              0x080   /* union */
 #define CT_FUNCTIONPTR        0x100   /* pointer to function */
 #define CT_VOID               0x200   /* void */
-#define CT_PRIMITIVE_COMPLEX  0x400   /* _cffi_float/double_complex_t */
+#define CT_PRIMITIVE_COMPLEX  0x400   /* float _Complex, double _Complex */
 
 /* other flags that may also be set in addition to the base flag: */
 #define CT_IS_VOIDCHAR_PTR     0x00001000
@@ -4728,8 +4728,8 @@ static PyObject *new_primitive_type(const char *name)
        EPTYPE(f, float, CT_PRIMITIVE_FLOAT )                    \
        EPTYPE(d, double, CT_PRIMITIVE_FLOAT )                   \
        EPTYPE(ld, long double, CT_PRIMITIVE_FLOAT | CT_IS_LONGDOUBLE ) \
-       EPTYPE2(fc, "_cffi_float_complex_t", cffi_float_complex_t, CT_PRIMITIVE_COMPLEX)\
-       EPTYPE2(dc, "_cffi_double_complex_t", cffi_double_complex_t, CT_PRIMITIVE_COMPLEX)\
+       EPTYPE2(fc, "float _Complex", cffi_float_complex_t, CT_PRIMITIVE_COMPLEX ) \
+       EPTYPE2(dc, "double _Complex", cffi_double_complex_t, CT_PRIMITIVE_COMPLEX ) \
        ENUM_PRIMITIVE_TYPES_WCHAR                               \
        EPTYPE2(c16, "char16_t", cffi_char16_t, CT_PRIMITIVE_CHAR ) \
        EPTYPE2(c32, "char32_t", cffi_char32_t, CT_PRIMITIVE_CHAR ) \
@@ -7656,13 +7656,14 @@ static int _testfunc23(char *p)
 }
 
 #if 0   /* libffi doesn't properly support complexes currently */
+        /* also, MSVC might not support _Complex... */
         /* if this is enabled one day, remember to also add _Complex
          * arguments in addition to return values. */
-static _cffi_float_complex_t _testfunc24(float a, float b)
+static float _Complex _testfunc24(float a, float b)
 {
     return a + I*2.0*b;
 }
-static _cffi_double_complex_t _testfunc25(double a, double b)
+static double _Complex _testfunc25(double a, double b)
 {
     return a + I*2.0*b;
 }
diff --git a/src/c/realize_c_type.c b/src/c/realize_c_type.c
index d9b9f19b..82629b7e 100644
--- a/src/c/realize_c_type.c
+++ b/src/c/realize_c_type.c
@@ -151,8 +151,8 @@ static PyObject *build_primitive_type(int num)
         "uint_fast64_t",
         "intmax_t",
         "uintmax_t",
-        "_cffi_float_complex_t",
-        "_cffi_double_complex_t",
+        "float _Complex",
+        "double _Complex",
         "char16_t",
         "char32_t",
     };
diff --git a/src/c/test_c.py b/src/c/test_c.py
index a86939f2..ced4f821 100644
--- a/src/c/test_c.py
+++ b/src/c/test_c.py
@@ -247,7 +247,7 @@ def test_float_types():
 def test_complex_types():
     INF = 1E200 * 1E200
     for name in ["float", "double"]:
-        p = new_primitive_type("_cffi_" + name + "_complex_t")
+        p = new_primitive_type(name + " _Complex")
         assert bool(cast(p, 0)) is False
         assert bool(cast(p, INF))
         assert bool(cast(p, -INF))
@@ -1246,7 +1246,7 @@ def test_call_function_9():
 
 def test_call_function_24():
     BFloat = new_primitive_type("float")
-    BFloatComplex = new_primitive_type("_cffi_float_complex_t")
+    BFloatComplex = new_primitive_type("float _Complex")
     BFunc3 = new_function_type((BFloat, BFloat), BFloatComplex, False)
     if 0:   # libffi returning nonsense silently, so logic disabled for now
         f = cast(BFunc3, _testfunc(24))
@@ -1260,7 +1260,7 @@ def test_call_function_24():
 
 def test_call_function_25():
     BDouble = new_primitive_type("double")
-    BDoubleComplex = new_primitive_type("_cffi_double_complex_t")
+    BDoubleComplex = new_primitive_type("double _Complex")
     BFunc3 = new_function_type((BDouble, BDouble), BDoubleComplex, False)
     if 0:   # libffi returning nonsense silently, so logic disabled for now
         f = cast(BFunc3, _testfunc(25))
@@ -4536,9 +4536,9 @@ def test_unaligned_types():
     buf = buffer(pbuf)
     #
     for name in ['short', 'int', 'long', 'long long', 'float', 'double',
-                 '_cffi_float_complex_t', '_cffi_double_complex_t']:
+                 'float _Complex', 'double _Complex']:
         p = new_primitive_type(name)
-        if name.endswith('_complex_t'):
+        if name.endswith(' _Complex'):
             num = cast(p, 1.23 - 4.56j)
         else:
             num = cast(p, 0x0123456789abcdef)