Diffraction on a body centered lattice, h+k+l even?

[Tom83B]

This is in my book:

$$exp[2\pi i(hx+ky+lz)][1+exp(\pi i(h+k+l))]=2exp[2\pi i(hx+ky+lz)]\cos^2[\frac{\pi}{2}(h+k+l)]$$

And in order for the cosine not to be zero, $$h+k+l$$ must be even when we want to see the reflection.

But I think that the result should be $$exp[2\pi i(hx+ky+lz)](2\cos^2[\frac{\pi}{2}(h+k+l)]+i\sin[\pi(h+k+l)])$$
Why isn't the imaginary part there? My idea was that we only need the real part, but because we multiply two complex numbers, I can't do this because $$i^2=-1$$, can I?

 

[johng23]

That does seem strange. What is this equation supposed to be anyway? For what purpose is the author converting the exponential to trig functions? Also, I recognize the (1+exp) factor as the structure factor for BCC, but I can't remember ever seeing it multiplied by a second exponential that way.

 

[Modulated]

What is the sine of an integer multiple of pi?

 

[Tom83B]

What is the sine of an integer multiple of pi?

Thank you very much :-)