1) check it...no matter wat value of n ..it is always coming out to be complex.. it might be conjugate in the denominator..
for tht.. divide and multiply the numerator and denominator by root2^2n and root2^2n+1 respectively.. it gets u euler form ..solve to get the power of e as npi... u will surely get the ans..
2) divide both equations by 2^n ...
u get e ^ { i npi/6} = e ^ - {i npi/6} thus it gets u e^ix - e^-ix = 0 form.. which means sinx is zero.. thus npi/6 = mpi.. least value of n is 6...