How many multiplications and additions does it take to compute an FFT of a signal?
If you are interested in more involved numbers of operations, you can check A modified split-radix FFT with fewer arithmetic operations, by Johnson and Frigo, IEEE Transactions on Signal Processing, 2007, authors of the &quot;Fastest Fourier Transform in the West&quot; (FFTW). For instance, they claim that the complexity of the classic radix-2 is about:
$$ 5N\log_2 N$$
while the split-radix yields:
$$4N \log_2 N − 6N + 8\,,$$
and they achieved the improvement:
$$\frac{34}{9} N \log_2 N − \frac{124 }{27 }N − 2 \log_2 N − \frac{2}{9}
(−1)^{\log_2 N} \log_2 N + \frac{16}{27}
 (−1)^{\log_2 N} + 8\,.$$
As said by others, you can see this number depends on implementations, and that the actual gain is subtle.