The electric and the magnetic field, associated with an e.m. wave, propagating along the +z-axis, can be represented by

In an electromagnetic wave, $\vec{E}$, $\vec{B}$ and the direction of propagation are mutually perpendicular, and the wave travels along $\vec{E}\times\vec{B}$.
For propagation along +z we need $\vec{E}\times\vec{B}$ along $\hat{k}$.
$\hat{i}\times\hat{j} = \hat{k}$, so $\vec{E} = E_0\hat{i}$, $\vec{B} = B_0\hat{j}$ gives propagation along +z.
Checking the others: $\hat{j}\times\hat{k} = \hat{i}$ (along +x), $\hat{k}\times\hat{i} = \hat{j}$ (along +y), $\hat{j}\times\hat{i} = -\hat{k}$ (along −z).
Hence $\vec{E} = E_0\hat{i}$, $\vec{B} = B_0\hat{j}$.