diff --git a/array_api_strict/_array_object.py b/array_api_strict/_array_object.py
index a917441..afee030 100644
--- a/array_api_strict/_array_object.py
+++ b/array_api_strict/_array_object.py
@@ -26,10 +26,12 @@
     _integer_dtypes,
     _integer_or_boolean_dtypes,
     _floating_dtypes,
+    _real_floating_dtypes,
     _complex_floating_dtypes,
     _numeric_dtypes,
     _result_type,
     _dtype_categories,
+    _real_to_complex_map,
 )
 from ._flags import get_array_api_strict_flags, set_array_api_strict_flags
 
@@ -243,6 +245,7 @@ def _promote_scalar(self, scalar):
         """
         from ._data_type_functions import iinfo
 
+        target_dtype = self.dtype
         # Note: Only Python scalar types that match the array dtype are
         # allowed.
         if isinstance(scalar, bool):
@@ -268,10 +271,13 @@ def _promote_scalar(self, scalar):
                     "Python float scalars can only be promoted with floating-point arrays."
                 )
         elif isinstance(scalar, complex):
-            if self.dtype not in _complex_floating_dtypes:
+            if self.dtype not in _floating_dtypes:
                 raise TypeError(
-                    "Python complex scalars can only be promoted with complex floating-point arrays."
+                    "Python complex scalars can only be promoted with floating-point arrays."
                 )
+            # 1j * array(floating) is allowed
+            if self.dtype in _real_floating_dtypes:
+                target_dtype = _real_to_complex_map[self.dtype]
         else:
             raise TypeError("'scalar' must be a Python scalar")
 
@@ -282,7 +288,7 @@ def _promote_scalar(self, scalar):
         # behavior for integers within the bounds of the integer dtype.
         # Outside of those bounds we use the default NumPy behavior (either
         # cast or raise OverflowError).
-        return Array._new(np.array(scalar, dtype=self.dtype._np_dtype), device=self.device)
+        return Array._new(np.array(scalar, dtype=target_dtype._np_dtype), device=self.device)
 
     @staticmethod
     def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
diff --git a/array_api_strict/_dtypes.py b/array_api_strict/_dtypes.py
index b51ed92..66304dd 100644
--- a/array_api_strict/_dtypes.py
+++ b/array_api_strict/_dtypes.py
@@ -126,6 +126,7 @@ def __hash__(self):
     "floating-point": _floating_dtypes,
 }
 
+_real_to_complex_map = {float32: complex64, float64: complex128}
 
 # Note: the spec defines a restricted type promotion table compared to NumPy.
 # In particular, cross-kind promotions like integer + float or boolean +
diff --git a/array_api_strict/tests/test_array_object.py b/array_api_strict/tests/test_array_object.py
index 4535d99..edfa073 100644
--- a/array_api_strict/tests/test_array_object.py
+++ b/array_api_strict/tests/test_array_object.py
@@ -108,6 +108,14 @@ def _check_op_array_scalar(dtypes, a, s, func, func_name, BIG_INT=BIG_INT):
     # - a Python int or float for real floating-point array dtypes
     # - a Python int, float, or complex for complex floating-point array dtypes
 
+    # an exception: complex scalar <op> floating array
+    scalar_types_for_float = [float, int]
+    if not (func_name.startswith("__i")
+            or (func_name in ["__floordiv__", "__rfloordiv__", "__mod__", "__rmod__"]
+                and type(s) == complex)
+    ):
+        scalar_types_for_float += [complex]
+
     if ((dtypes == "all"
          or dtypes == "numeric" and a.dtype in _numeric_dtypes
          or dtypes == "real numeric" and a.dtype in _real_numeric_dtypes
@@ -121,7 +129,7 @@ def _check_op_array_scalar(dtypes, a, s, func, func_name, BIG_INT=BIG_INT):
         # isinstance here.
         and (a.dtype in _boolean_dtypes and type(s) == bool
              or a.dtype in _integer_dtypes and type(s) == int
-             or a.dtype in _real_floating_dtypes and type(s) in [float, int]
+             or a.dtype in _real_floating_dtypes and type(s) in scalar_types_for_float
              or a.dtype in _complex_floating_dtypes and type(s) in [complex, float, int]
         )):
         if a.dtype in _integer_dtypes and s == BIG_INT:
diff --git a/array_api_strict/tests/test_elementwise_functions.py b/array_api_strict/tests/test_elementwise_functions.py
index 0b90f0b..cc3a2cd 100644
--- a/array_api_strict/tests/test_elementwise_functions.py
+++ b/array_api_strict/tests/test_elementwise_functions.py
@@ -233,15 +233,25 @@ def _array_vals():
         if nargs(func) != 2:
             continue
 
+        nocomplex = [
+            'atan2', 'copysign', 'floor_divide', 'hypot', 'logaddexp',  'nextafter',
+            'remainder',
+            'greater', 'less', 'greater_equal', 'less_equal', 'maximum', 'minimum',
+        ]
+
         for s in [1, 1.0, 1j, BIG_INT, False]:
             for a in _array_vals():
                 for func1 in [lambda s: func(a, s), lambda s: func(s, a)]:
-                    allowed = _check_op_array_scalar(dtypes, a, s, func1, func_name)
+
+                    if func_name in nocomplex and type(s) == complex:
+                        allowed = False
+                    else:
+                        allowed = _check_op_array_scalar(dtypes, a, s, func1, func_name)
 
                     # only check `func(array, scalar) == `func(array, array)` if
                     # the former is legal under the promotion rules
                     if allowed:
-                        conv_scalar = asarray(s, dtype=a.dtype)
+                        conv_scalar = a._promote_scalar(s)
 
                         with suppress_warnings() as sup:
                             # ignore warnings from pow(BIG_INT)