What is the difference between real and imaginary parts of a sinusoid? Can somebody explain, without using complicated mathematical formulas, what do real and imaginary parts of the sinus function represent?
And what are relations between them?
I cannot understand why there are differences in shape when I look the spectrum. I noticed that the maximum height of green (imaginary) line is 6,6 mm on my display while the red is cca 1/2 of the green. I thought if could it simply mean that the green represents difference between maximums of the sinusoid, e.g. 25 and -25. I cannot understand why the shape of these line is such and not like the black one. Why it is mirrored? Images welcome.
This is image which I am referring to:

 A: I have found article where the Fourier transform is greatly explained:

The Fourier Transform produces a complex number valued output image which can be displayed with two images, either with the real and imaginary part or with magnitude and phase.
  In image processing, often only the magnitude of the Fourier Transform is displayed, as it contains most of the information of the geometric structure of the spatial domain image. However, if we want to re-transform the Fourier image into the correct spatial domain after some processing in the frequency domain, we must make sure to preserve both magnitude and phase of the Fourier image. 

Source: http://homepages.inf.ed.ac.uk/rbf/HIPR2/fourier.htm
So the real and imaginary numbers can be negative numbers, which in digital image processing cannot be displayed. From the comments above and other sources  I came to conclusion that real and imaginary components of the Fourier Transform comprise from sinus and cosine waves. The black curve on image is magnitude, which is positive number scaled with logarithm*. * - Now, here I am not sure what the term scale exactly means. I have two possibilities: either it scales (zooms) the curve to be better visible or it shifts the curve "upwards" by adding number so that all the values are positive, not negative. 
Another question stays opened: If we have 4 images / 4 sets of data, why the curve does not contain 4 curves? Probably author of the program (http://lodev.org/cgtutor/fourier.html) Joined the two components of magnitude & phase together? I don't understand his FFT algorithm that much because it differs from standard formulas:
$$G(n)=\frac{1}{N}\sum_{x=0}^{N-1}g(x)e^{-i2 \pi \frac{n}{N}x}$$(http://www.fmwconcepts.com/imagemagick/fourier_transforms/images/fft_1d_equation.jpg)
