Understanding complex fft results

1. Why does FFT return complex numbers?
2. What do you understand about complex Fourier transform?
3. What does magnitude of FFT tell you?

Why does FFT return complex numbers?

It's because processing periodic signals involves trigonometry all the time, and there is a simple way to move from sines and cosines to more simple complex numbers algebra: Euler's formula. So most of the time signals are just converted to their complex exponential form.

What do you understand about complex Fourier transform?

Each transform has an analysis equation (also called the forward transform) and a synthesis equation (also called the inverse transform). The analysis equations describe how to calculate each value in the frequency domain based on all of the values in the time domain.

What does magnitude of FFT tell you?

The output of the FFT is a complex vector containing information about the frequency content of the signal. The magnitude tells you the strength of the frequency components relative to other components. The phase tells you how all the frequency components align in time.