Complexity of FFT Algorithm

Question

OkayI am using iterative FFT algorithm and I have found that since there are 2N computation per stage and there are logN stages the complexity should be O(2NlogN) I can reduce the number of multiplication per stage to N/2 So the total complexity becomes O((3N/2)logN)

So discarding the constant factors the algorithm still has complexity O(NlogN)?

Answer 1

For any constant $c$. $O(c N\log N)=O(N\log N)$.