diff --git a/spec/API_specification/array_api/linalg.py b/spec/API_specification/array_api/linalg.py
index b3595e1fa..d5d7780ef 100644
--- a/spec/API_specification/array_api/linalg.py
+++ b/spec/API_specification/array_api/linalg.py
@@ -500,7 +500,7 @@ def vector_norm(x: array, /, *, axis: Optional[Union[int, Tuple[int, ...]]] = No
     Parameters
     ----------
     x: array
-        input array. Should have a real-valued floating-point data type.
+        input array. Should have a floating-point data type.
     axis: Optional[Union[int, Tuple[int, ...]]]
         If an integer, ``axis`` specifies the axis (dimension) along which to compute vector norms. If an n-tuple, ``axis`` specifies the axes (dimensions) along which to compute batched vector norms. If ``None``, the vector norm must be computed over all array values (i.e., equivalent to computing the vector norm of a flattened array). Negative indices must be supported. Default: ``None``.
     keepdims: bool
@@ -541,7 +541,7 @@ def vector_norm(x: array, /, *, axis: Optional[Union[int, Tuple[int, ...]]] = No
     Returns
     -------
     out: array
-        an array containing the vector norms. If ``axis`` is ``None``, the returned array must be a zero-dimensional array containing a vector norm. If ``axis`` is a scalar value (``int`` or ``float``), the returned array must have a rank which is one less than the rank of ``x``. If ``axis`` is a ``n``-tuple, the returned array must have a rank which is ``n`` less than the rank of ``x``. The returned array must have a real-valued floating-point data type determined by :ref:`type-promotion`.
+        an array containing the vector norms. If ``axis`` is ``None``, the returned array must be a zero-dimensional array containing a vector norm. If ``axis`` is a scalar value (``int`` or ``float``), the returned array must have a rank which is one less than the rank of ``x``. If ``axis`` is a ``n``-tuple, the returned array must have a rank which is ``n`` less than the rank of ``x``. If ``x`` has a real-valued data type, the returned array must have a real-valued floating-point data type determined by :ref:`type-promotion`. If ``x`` has a complex-valued data type, the returned array must have a real-valued floating-point data type whose precision matches the precision of ``x`` (e.g., if ``x`` is ``complex128``, then the returned array must have a ``float64`` data type).
     """
 
 __all__ = ['cholesky', 'cross', 'det', 'diagonal', 'eigh', 'eigvalsh', 'inv', 'matmul', 'matrix_norm', 'matrix_power', 'matrix_rank', 'matrix_transpose', 'outer', 'pinv', 'qr', 'slogdet', 'solve', 'svd', 'svdvals', 'tensordot', 'trace', 'vecdot', 'vector_norm']