$\operatorname{adj}(R + i\Theta) = R^{\mathsf T} - i\Theta$

Let $R^{(\varsigma)}(r) = \begin{pmatrix} R_0 & R_1 \\ -R_1 & R_0\end{pmatrix}$ and $\Theta^{(\varsigma)}(\theta) = \begin{pmatrix} \Theta_0 & \Theta_1 \\ \Theta_1 & -\Theta_0\end{pmatrix}$ be the radial and angular coefficient matrices written after Hintz eq. (7), with the explicit coefficients $R_0,R_1,\Theta_0,\Theta_1$ of the paper. Then for every $(r,\theta)$

the identity $\operatorname{adj}C = R^{\mathsf T} - i\Theta$ stated in the paper, proved directly from the $2\times 2$ adjugate formula and the symmetry pattern of $R$ and $\Theta$.