Introduction:
The FFT (Fast Fourier Transform) algorithm is a widely used algorithm in various fields, including signal processing, image processing, and communication systems. It is primarily used to perform complex operations, specifically the calculation of the discrete Fourier transform (DFT) and its inverse (IDFT).

Explanation:
The FFT algorithm is designed to efficiently compute the DFT of a sequence or signal, which is a mathematical transformation that converts a time-domain signal into its frequency-domain representation. The DFT is defined as a sum of complex exponential functions, and the FFT algorithm allows us to calculate this sum efficiently by exploiting the symmetry and periodicity properties of the complex exponential functions.

Key Features of the FFT algorithm:
1. Efficiency: The FFT algorithm is significantly faster than the direct computation of the DFT. It reduces the computational complexity from O(N^2) to O(N log N), where N is the number of samples in the input sequence.
2. Decomposition: The FFT algorithm decomposes the DFT calculation into smaller sub-problems, allowing for efficient computation through a divide-and-conquer approach.
3. Radix-2 Cooley-Tukey Algorithm: The most commonly used variant of the FFT algorithm is the Radix-2 Cooley-Tukey algorithm, which recursively divides the input sequence into smaller sub-sequences and combines their DFTs to obtain the final result.
4. Complexity: The FFT algorithm operates on complex numbers, which consist of a real and imaginary part. It can handle complex signals and provide information about both the magnitude and phase of the frequency components.
5. Inverse Transform: The FFT algorithm can also perform the inverse Fourier transform, which converts a frequency-domain representation back to the time-domain. This is useful for reconstructing a signal from its frequency components.

Conclusion:
In conclusion, the statement that the FFT algorithm is designed to perform complex operations is true. It efficiently computes the complex DFT and IDFT of a sequence or signal, providing valuable information about its frequency components. The FFT algorithm's efficiency, decomposition, and complexity make it an essential tool in various applications, enabling tasks such as spectral analysis, filtering, modulation, and compression.