diff --git a/doc/user-guide/complex-numbers.rst b/doc/user-guide/complex-numbers.rst
new file mode 100644
index 00000000000..e62b9d6f8d8
--- /dev/null
+++ b/doc/user-guide/complex-numbers.rst
@@ -0,0 +1,124 @@
+.. currentmodule:: xarray
+
+.. _complex:
+
+Complex Numbers
+===============
+
+Xarray leverages NumPy to seamlessly handle complex numbers in :py:class:`~xarray.DataArray` and :py:class:`~xarray.Dataset` objects.
+
+In the examples below, we are using a DataArray named ``da`` with complex elements (of :math:`\mathbb{C}`):
+
+.. ipython:: python
+
+    import xarray as xr
+    import numpy as np
+
+    data = np.array([[1 + 2j, 3 + 4j], [5 + 6j, 7 + 8j]])
+    da = xr.DataArray(
+        data,
+        dims=["x", "y"],
+        coords={"x": ["a", "b"], "y": [1, 2]},
+        name="complex_nums",
+    )
+
+
+Operations on Complex Data
+--------------------------
+You can access real and imaginary components using the ``.real`` and ``.imag`` attributes. Most NumPy universal functions (ufuncs) like :py:doc:`numpy.abs <numpy:reference/generated/numpy.absolute>` or :py:doc:`numpy.angle <numpy:reference/generated/numpy.angle>` work directly.
+
+.. ipython:: python
+
+    da.real
+    np.abs(da)
+
+.. note::
+    Like NumPy, ``.real`` and ``.imag`` typically return *views*, not copies, of the original data.
+
+
+Reading and Writing Complex Data
+--------------------------------
+
+Writing complex data to NetCDF files (see :ref:`io.netcdf`) is supported via :py:meth:`~xarray.DataArray.to_netcdf` using specific backend engines that handle complex types:
+
+
+.. tab:: h5netcdf
+
+   This requires the `h5netcdf <https://h5netcdf.org>`_ library to be installed.
+
+   .. ipython:: python
+       :okwarning:
+
+       # write the data to disk
+       da.to_netcdf("complex_nums_h5.nc", engine="h5netcdf")
+       # read the file back into memory
+       ds_h5 = xr.open_dataset("complex_nums_h5.nc", engine="h5netcdf")
+       # check the dtype
+       ds_h5[da.name].dtype
+
+
+.. tab:: netcdf4
+
+   Requires the `netcdf4-python (>= 1.7.1) <https://github.com/Unidata/netcdf4-python>`_ library and you have to enable ``auto_complex=True``.
+
+   .. ipython:: python
+       :okwarning:
+
+       # write the data to disk
+       da.to_netcdf("complex_nums_nc4.nc", engine="netcdf4", auto_complex=True)
+       # read the file back into memory
+       ds_nc4 = xr.open_dataset(
+           "complex_nums_nc4.nc", engine="netcdf4", auto_complex=True
+       )
+       # check the dtype
+       ds_nc4[da.name].dtype
+
+
+.. warning::
+   The ``scipy`` engine only supports NetCDF V3 and does *not* support complex arrays; writing with ``engine="scipy"`` raises a ``TypeError``.
+
+
+Alternative: Manual Handling
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+If direct writing is not supported (e.g., targeting NetCDF3), you can manually
+split the complex array into separate real and imaginary variables before saving:
+
+.. ipython:: python
+
+    # Write data to file
+    ds_manual = xr.Dataset(
+        {
+            f"{da.name}_real": da.real,
+            f"{da.name}_imag": da.imag,
+        }
+    )
+    ds_manual.to_netcdf("complex_manual.nc", engine="scipy")  # Example
+
+    # Read data from file
+    ds = xr.open_dataset("complex_manual.nc", engine="scipy")
+    reconstructed = ds[f"{da.name}_real"] + 1j * ds[f"{da.name}_imag"]
+
+Recommendations
+^^^^^^^^^^^^^^^
+
+- Use ``engine="netcdf4"`` with ``auto_complex=True`` for full compliance and ease.
+- Use ``h5netcdf`` for HDF5-based storage when interoperability with HDF5 is desired.
+- For maximum legacy support (NetCDF3), manually handle real/imaginary components.
+
+.. ipython:: python
+    :suppress:
+
+    # Cleanup
+    import os
+
+    for f in ["complex_nums_nc4.nc", "complex_nums_h5.nc", "complex_manual.nc"]:
+        if os.path.exists(f):
+            os.remove(f)
+
+
+
+See also
+--------
+- :ref:`io.netcdf` — full NetCDF I/O guide
+- `NumPy complex numbers <https://numpy.org/doc/stable/user/basics.types.html#complex>`__
diff --git a/doc/user-guide/index.rst b/doc/user-guide/index.rst
index d8c4964457b..92f73c380c6 100644
--- a/doc/user-guide/index.rst
+++ b/doc/user-guide/index.rst
@@ -27,4 +27,5 @@ examples that describe many common tasks that you can accomplish with xarray.
    options
    testing
    duckarrays
+   complex-numbers
    hierarchical-data
diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index e0a9853ee45..4e6bf5a8bd1 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -48,6 +48,9 @@ Documentation
 - Fix references to core classes in docs (:issue:`10195`, :pull:`10207`).
   By `Mattia Almansi <https://github.com/malmans2>`_.
 
+- Add a dedicated 'Complex Numbers' sections to the User Guide (:issue:`10213`, :pull:`10235`).
+  By `Andre Wendlinger <https://github.com/andrewendlinger>`_.
+
 Internal Changes
 ~~~~~~~~~~~~~~~~