defines a class in $H^1(B^3_{x_2+x_3},W)$, we must compute its image under the differential in the Gersten-Witt complex associated to $B^3_{x_2+x_3}$. The image of $(\kappa({\mathfrak q_1}),(x_0x_1+x_2)\rho_{x_0^2+1})$ is the localization in the minimal prime ideals of its support of the complete intersection module $M_1:=B^3_{x_2+x_3}/(x_0^2+1,x_0x_1+x_2)$ endowed with the symmetric isomorphism $$\rho_{x_0^2+1,x_0x_1+x_2}:M_1\to \exten 2{B^3_{x_2+x_3}}{M_1}{B^3_{x_2+x_3}}$$ defined by $\rho_{x_0^2+1,x_0x_1+x_2}(1)=Kos(x_0^2+1,x_0x_1+x_2)$, where the latter is the Koszul complex given by the regular sequence $(x_0^2+1,x_0x_1+x_2)$. It follows from the discussion above that the only minimal prime ideal in the support of $M_1$ is $(x_1,x_2)$. To compute the localization of $M_1$ and $\rho_{x_0^2+1,x_0x_1+x_2}$ in the prime ideal $(x_1,x_2)$ we compare the regular sequences $(x_0^2+1,x_0x_1+x_2)$ and $(x_1,x_2)$. Since $x_0^2+1=x_2x_3-x_1^2$ in $B^3$, we get $$\begin{pmatrix} -x_1 & x_3 \\ x_0 & 1\end{pmatrix}\begin{pmatrix} x_1 \\ x_2\end{pmatrix}=\begin{pmatrix} x_0^2+1 \\ x_0x_1+x_2\end{pmatrix}.$$ The determinant of the matrix is $-x_1-x_0x_3$, which is not in the ideal $(x_1,x_2)$ and therefore the regular sequences $(x_0^2+1,x_0x_1+x_2)$ and $(x_1,x_2)$ generate the same ideal in $B^3_{(x_1,x_2)}$ and $Kos(x_0^2+1,x_0x_1+x_2)=(-x_1-x_0x_3)Kos(x_1,x_2)$. Since the residue field at the prime ideal $(x_1,x_2)$ is $\C(x_3)$ and the class of $-x_1-x_0x_3$ in this field is $-ix_3$, we see that the image of $(\kappa({\mathfrak q_1}),(x_0x_1+x_2)\rho_{x_0^2+1})$ under the differential in the Gersten-Witt complex is the symmetric isomorphism $$\C(x_3)\to \exten 2{B^3_{(x_1,x_2)}}{\C(x_3)}{B^3_{(x_1,x_2)}}$$ defined 