diff --git a/builtins/2.7/cmath.pyi b/builtins/2.7/cmath.pyi
index 2364aeeb5..9bca157b7 100644
--- a/builtins/2.7/cmath.pyi
+++ b/builtins/2.7/cmath.pyi
@@ -1,48 +1,30 @@
 """Stub file for the 'cmath' module."""
-# This is an autogenerated file. It serves as a starting point
-# for a more precise manual annotation of this module.
-# Feel free to edit the source below, but remove this header when you do.
 
-from typing import Any, List, Tuple, Dict, Generic
+from typing import Union
 
-def acos(*args, **kwargs) -> complex: ...
+e = ...  # type: float
+pi = ...  # type: float
 
-def acosh(*args, **kwargs) -> complex: ...
+_C = Union[float, complex]
 
-def asin(*args, **kwargs) -> complex: ...
-
-def asinh(*args, **kwargs) -> complex: ...
-
-def atan(*args, **kwargs) -> complex: ...
-
-def atanh(*args, **kwargs) -> complex: ...
-
-def cos(*args, **kwargs) -> complex: ...
-
-def cosh(*args, **kwargs) -> complex: ...
-
-def exp(*args, **kwargs) -> complex: ...
-
-def isinf(a: complex) -> bool: ...
-
-def isnan(a: complex) -> bool: ...
-
-def log(a: complex, *args, **kwargs) -> complex: ...
-
-def log10(*args, **kwargs) -> complex: ...
-
-def phase(a: complex) -> float: ...
-
-def polar(a: complex) -> tuple: ...
-
-def rect(a: float, b: float) -> complex: ...
-
-def sin(*args, **kwargs) -> complex: ...
-
-def sinh(*args, **kwargs) -> complex: ...
-
-def sqrt(*args, **kwargs) -> complex: ...
-
-def tan(*args, **kwargs) -> complex: ...
-
-def tanh(*args, **kwargs) -> complex: ...
+def acos(x:_C) -> complex: ...
+def acosh(x:_C) -> complex: ...
+def asin(x:_C) -> complex: ...
+def asinh(x:_C) -> complex: ...
+def atan(x:_C) -> complex: ...
+def atanh(x:_C) -> complex: ...
+def cos(x:_C) -> complex: ...
+def cosh(x:_C) -> complex: ...
+def exp(x:_C) -> complex: ...
+def isinf(z:_C) -> bool: ...
+def isnan(z:_C) -> bool: ...
+def log(x:_C, base:_C = ...) -> complex: ...
+def log10(x:_C) -> complex: ...
+def phase(z:_C) -> float: ...
+def polar(z:_C) -> Tuple[float, float]: ...
+def rect(r:float, phi:float) -> complex: ...
+def sin(x:_C) -> complex: ...
+def sinh(x:_C) -> complex: ...
+def sqrt(x:_C) -> complex: ...
+def tan(x:_C) -> complex: ...
+def tanh(x:_C) -> complex: ...