Use of complex number to resolve a practical problem

In analyzing the tuning response of visual cortex neurons, there is a need to find the preferred direction and the opposition as well as orthognal directions. This is not an easy task, but could be conveniently achieved by using complex numbers. When you find the preferred direction through gaussian fitting, you could create a complex vector y1Tmp=exp(1i*(y1-1)*2*pi/angleNO). Then find the opposition direction:y2=angle(y1Tmp*exp(1i*pi)). The orthognal direction is y3=angle(y1Tmp*exp(1i*pi/2)). And the other orthognal direction is y4=angle(y1Tmp*exp(-1i*pi/2)). This way we could easily calculate the Orientation Selectivity of neurons.