Why are the basis functions for DFT so?
If you look at the idea of Continuous Time Fourier Series (CTFT), it says any periodic signal can be constructed by summation of infinite number of complex exponentials. But in descrete case , only 'N' different  complex exponentials are enough , because there are only 'N' distinct complex  exponentials exists (N is the period of discrete signal). 

DFT is nothing but DFS (Discrete Fourier Series).So You can extend the 
same idea to get the answer.