diff --git a/chapter1/complex_mode.ipynb b/chapter1/complex_mode.ipynb
index 3f7c8310..0fb38eed 100644
--- a/chapter1/complex_mode.ipynb
+++ b/chapter1/complex_mode.ipynb
@@ -34,7 +34,8 @@
     "We now need to define our inner product space.\n",
     "We choose the $L^2$ inner product spaces, which is a _[sesquilinear](https://en.wikipedia.org/wiki/Sesquilinear_form) 2-form_,\n",
     "meaning that $\\langle u, v\\rangle$ is a map from $V_h\\times V_h\\mapsto K$, and\n",
-    "$\\langle u, v \\rangle = \\int_\\Omega u \\cdot \\bar v ~\\mathrm{d} x$. As it is sesquilinear, we have the following properties:\n",
+    "$\\langle u, v \\rangle = \\int_\\Omega u \\cdot \\bar v ~\\mathrm{d} x$.\n",
+    "As it is sesquilinear, we have the following properties:\n",
     "\n",
     "$$\n",
     "\\begin{align}\n",
@@ -243,7 +244,7 @@
     "x = ufl.SpatialCoordinate(mesh)\n",
     "u_ex = 0.5 * x[0] ** 2 + 1j * x[1] ** 2\n",
     "L2_error = dolfinx.fem.form(\n",
-    "    ufl.dot(uh - u_ex, uh - u_ex) * ufl.dx(metadata={\"quadrature_degree\": 5})\n",
+    "    ufl.inner(uh - u_ex, uh - u_ex) * ufl.dx(metadata={\"quadrature_degree\": 5})\n",
     ")\n",
     "local_error = dolfinx.fem.assemble_scalar(L2_error)\n",
     "global_error = np.sqrt(mesh.comm.allreduce(local_error, op=MPI.SUM))\n",
diff --git a/chapter1/complex_mode.py b/chapter1/complex_mode.py
index ba5f68f2..6349163a 100644
--- a/chapter1/complex_mode.py
+++ b/chapter1/complex_mode.py
@@ -42,7 +42,8 @@
 # We now need to define our inner product space.
 # We choose the $L^2$ inner product spaces, which is a _[sesquilinear](https://en.wikipedia.org/wiki/Sesquilinear_form) 2-form_,
 # meaning that $\langle u, v\rangle$ is a map from $V_h\times V_h\mapsto K$, and
-# $\langle u, v \rangle = \int_\Omega u \cdot \bar v ~\mathrm{d} x$. As it is sesquilinear, we have the following properties:
+# $\langle u, v \rangle = \int_\Omega u \cdot \bar v ~\mathrm{d} x$.
+# As it is sesquilinear, we have the following properties:
 #
 # $$
 # \begin{align}
@@ -166,7 +167,7 @@
 x = ufl.SpatialCoordinate(mesh)
 u_ex = 0.5 * x[0] ** 2 + 1j * x[1] ** 2
 L2_error = dolfinx.fem.form(
-    ufl.dot(uh - u_ex, uh - u_ex) * ufl.dx(metadata={"quadrature_degree": 5})
+    ufl.inner(uh - u_ex, uh - u_ex) * ufl.dx(metadata={"quadrature_degree": 5})
 )
 local_error = dolfinx.fem.assemble_scalar(L2_error)
 global_error = np.sqrt(mesh.comm.allreduce(local_error, op=MPI.SUM))