The electric-field complex-amplitude vector for a monochromatic wave traveling in free \text { space is } \mathbf{E}(\mathbf{r})=\hat{\mathbf{x}} E_{0} \sin (\beta y) \exp (-i \beta z) \text { . } Derive

an expression for the magnetic-field complex-amplitude vector. - Determine the direction of the flow of optical power. This wave may be regarded as the sum of two transverse electromagnetic waves.Identify them and determine their directions of propagation.