When should we use the full Gabor Function and when do we use only the real part?
The real part of the complex Gabor function is symmetric. This means it will give a large response at the centre of symmetric features such as lines. 

The imaginary part of the complex Gabor function is anti-symmetric. This means it will give a large response at the centre of anti-symmetric features such as edges.

The real and imaginary parts are sort of in quadrature. This means when you take the magnitude of the response to the complex Gabor filter it will be high at the location of both edge and line features, which can be useful.