Graduate Don't understand this function, s(cosξ + j sinξ) in my textbook

[FrankJ777]

My textbook for Advanced Electomagnetics, by Balinas has this identity.

cos θ = se^(jξ) = s( cos ξ + j sin ξ ).

I have no idea what they are saying. Is there an S funtion I'm not aware of?
I've looked back and forth, and he doesn't seem to explain it's use.

I've inserted a picture of the page, to provide context.
Hope I'm in the right section.

 

[anuttarasammyak]

I assume $j^2=-1$, right ? Then s is magnitude of complex number $cos\theta_l$ and $\zeta$ is its angle in Gauss plane.

 

[mfb]

s is just a constant, and they use Euler's formula to convert the complex exponential.

 

[FrankJ777]

So they are just saying that cos θ can be se^(jξ) = s( cos ξ + j sin ξ ). Where s is any old constant?
They're just decomposing cos θ into a real and imaginary part?

 

[DrClaude]

They're just decomposing cos θ into a real and imaginary part?

Yes.