Theoretical physics: Transverse vector wave-elliptically polarized?

Good morning! I have to work on a problem that I don't fully understand. I also posted it on nanolounge, but I haven't received a response yet. https://www.nanolounge.de/40782/beliebige-transversale-ektorwelle-elliptical-polarized I add my task and problem here Task: Here is my problem: