Infinite Well with Schrodinger equation

[PsychonautQQ]

Homework Statement

I'm having a bit of trouble following my textbook, I was under the impression ψ(x) = e^i(kx) = Cos(kx) + iSin(kx) but in my textbook they write the general solution to this equation as ψ(x) = ASin(kx) + BCos(kx). How come they wrote the sin part as not imaginary? isn't this suppose to be a complex number? I know this example is like the most common example for introduction to quantum physics classes so I'm hoping somebody can give me some insight here

 

[mfb]

A and B are complex numbers.
A=i and B=1 is a special case of the more general solution.

 

[PsychonautQQ]

A and B are complex numbers.
A=i and B=1 is a special case of the more general solution.

A and B are BOTH complex numbers? oh geeez this stuff is more confusing than i thought!