What does it mean to have an complex transmission angle?

[thatsmessedup]

I am getting a complex number for my transmission angle in part (c) but I do not know what that means. Am I even doing this correctly? Any help will be greatly appreciated. Thanks!

 

[tech99]

I am getting a complex number for my transmission angle in part (c) but I do not know what that means. Am I even doing this correctly? Any help will be greatly appreciated. Thanks!

View attachment 251875
View attachment 251876

When a wave crosses between media, we can see a surface wave. This is a guided wave traveling along the interface, having a field component in the direction of propagation. This component is in quadrature to the main wave. In effect, the E field vector becomes an ellipse.

 

[thatsmessedup]

So to get my Ktz, I will plug the complex number into cos(), slap a K0 in front and call it a day?