Let N be the number of complex numbers z with the properties that |z|=1 and z^{6 !}-z^{5 !} is a real number. Find the remainder when N is divided by 1000 .
Let N be the number of complex numbers z with the properties that |z|=1 and z^{6 !}-z^{5 !} is a real number. Find the remainder when N is divided by 1000 .