The radix-2 FFT algorithm is a widely used algorithm for computing the discrete Fourier transform (DFT) of a sequence of N complex numbers. The algorithm is based on the divide-and-conquer approach and is known for its efficiency in terms of time complexity.

The radix-2 FFT algorithm divides the N-point DFT into smaller DFTs of size N/2, recursively applies the algorithm to these smaller DFTs, and then combines the results to obtain the final DFT. This process is repeated until the size of the DFT becomes 2, at which point the DFT can be directly computed using a simple formula.

To calculate the total number of complex multiplications required by the radix-2 FFT algorithm, we can consider the number of complex multiplications needed at each stage of the algorithm.

1. Stage 1:
- At this stage, the N-point DFT is divided into two N/2-point DFTs.
- Each N/2-point DFT requires N/2 complex multiplications.
- Therefore, the total number of complex multiplications at this stage is N/2.

2. Stage 2:
- At this stage, each N/2-point DFT is further divided into two N/4-point DFTs.
- Each N/4-point DFT requires N/4 complex multiplications.
- Since there are two N/2-point DFTs, the total number of complex multiplications at this stage is 2(N/4) = N/2.

3. Stage 3:
- This stage follows the same pattern as stage 2, where each N/4-point DFT is divided into two N/8-point DFTs.
- Each N/8-point DFT requires N/8 complex multiplications.
- Since there are four N/4-point DFTs, the total number of complex multiplications at this stage is 4(N/8) = N/2.

4. Stage k:
- Following the same pattern, each N/(2^k) point DFT requires N/(2^k) complex multiplications.
- Since there are 2^(k-1) DFTs of size N/(2^k), the total number of complex multiplications at this stage is 2^(k-1)(N/(2^k)) = N/2.

The total number of stages required in the radix-2 FFT algorithm is log2(N), where log2 represents the logarithm to the base 2. Therefore, the total number of complex multiplications can be calculated by summing up the number of complex multiplications at each stage:

Total number of complex multiplications = N/2 + N/2 + N/2 + ... (log2(N) terms)
= (log2(N))(N/2)
= (N/2)log2(N)

Hence, option A, (N/2)log2(N), is the correct answer.