Lack of odd symmetry in imaginary component of fft

[MSchmeisser1]

I am trying to implement an algorithm that takes advantage of the odd symmetry that occurs in the imaginary bit of an fft of a real signal.
However when doing an fft of a simple cosine I correctly see even symmetry in the real part but no signals at all in the imaginary part. A sanity check in octave shows that an fft of a real signal should give even symmetry in the real part and odd symmetry in the imaginary part.

Attached is a plot of a 4096 point fft of a 1200hz cosine wave sampled at 4096hz.
The purple plot is the real bit, and the teal is the imaginary bit offset for clarity.

Am i misunderstanding something?

Here is the same in octave.