diff --git a/array_api_tests/test_data_type_functions.py b/array_api_tests/test_data_type_functions.py
index 34c40024..49898b6e 100644
--- a/array_api_tests/test_data_type_functions.py
+++ b/array_api_tests/test_data_type_functions.py
@@ -2,7 +2,7 @@
 from typing import Union
 
 import pytest
-from hypothesis import given
+from hypothesis import given, assume
 from hypothesis import strategies as st
 
 from . import _array_module as xp
@@ -23,26 +23,43 @@ def float32(n: Union[int, float]) -> float:
     return struct.unpack("!f", struct.pack("!f", float(n)))[0]
 
 
+def _float_match_complex(complex_dtype):
+    return xp.float32 if complex_dtype == xp.complex64 else xp.float64
+
+
 @given(
-    x_dtype=non_complex_dtypes(),
-    dtype=non_complex_dtypes(),
+    x_dtype=hh.all_dtypes,
+    dtype=hh.all_dtypes,
     kw=hh.kwargs(copy=st.booleans()),
     data=st.data(),
 )
 def test_astype(x_dtype, dtype, kw, data):
+    _complex_dtypes = (xp.complex64, xp.complex128)
+
     if xp.bool in (x_dtype, dtype):
         elements_strat = hh.from_dtype(x_dtype)
     else:
-        m1, M1 = dh.dtype_ranges[x_dtype]
-        m2, M2 = dh.dtype_ranges[dtype]
+
         if dh.is_int_dtype(x_dtype):
             cast = int
-        elif x_dtype == xp.float32:
+        elif x_dtype in (xp.float32, xp.complex64):
             cast = float32
         else:
             cast = float
+
+        real_dtype = x_dtype
+        if x_dtype in _complex_dtypes:
+            real_dtype = _float_match_complex(x_dtype)
+        m1, M1 = dh.dtype_ranges[real_dtype]
+
+        real_dtype = dtype
+        if dtype in _complex_dtypes:
+            real_dtype = _float_match_complex(x_dtype)
+        m2, M2 = dh.dtype_ranges[real_dtype]
+
         min_value = cast(max(m1, m2))
         max_value = cast(min(M1, M2))
+
         elements_strat = hh.from_dtype(
             x_dtype,
             min_value=min_value,
@@ -54,6 +71,11 @@ def test_astype(x_dtype, dtype, kw, data):
         hh.arrays(dtype=x_dtype, shape=hh.shapes(), elements=elements_strat), label="x"
     )
 
+    # according to the spec, "Casting a complex floating-point array to a real-valued
+    # data type should not be permitted."
+    # https://data-apis.org/array-api/latest/API_specification/generated/array_api.astype.html#astype
+    assume(not ((x_dtype in _complex_dtypes) and (dtype not in _complex_dtypes)))
+
     out = xp.astype(x, dtype, **kw)
 
     ph.assert_kw_dtype("astype", kw_dtype=dtype, out_dtype=out.dtype)