On our GitHub web page, we have made available a fully worked Matlab implementation of a radix-4 Decimation in Frequency FFT algorithm.
In the code, we have also provided an overall operations count in terms of complex matrix multiplications and additions.
It can be indeed shown that each radix-4 butterfly involves 3 complex multiplications and 8 complex additions.
Since there are log4N = log2N / 2 stages and each stage involves N / 4 butterflies, so the operations count is
complex multiplications = (3 / 8) * N * log2(N) complex additions = N * log2(N)