I am probably being really dense in this situation, but I cannot work out why the answer to the question is logical. The question is this:
Employ the definition $$\psi=E+icB $$ to show that $i\frac{d\psi}{dt}=c\nabla \times \psi $. (This bit is fine.) Assuming that $\psi \propto \psi_0e^{ikx-i\omega t}$ find the normalised plane-wave solutions with the magnetic field of $\psi_0$ along the z-axis and calculate their associated currents.
The answer is as follows: The plane-wave substitution provides the Eigen-equation \begin{equation} \omega \psi_0 = ick\hat{x} \times \psi_0, \end{equation}which is solved by \begin{equation} \psi_0 = \frac{1}{\sqrt{2}}(\hat{y}+i\hat{z}) =\pm \frac{\omega}{c}. \end{equation}
If anybody could help explain then I would be grateful!