 # Real and immaginary part of SLC product

Hello,
I am new in radar and I have a naive doubt. As explained in

Moreira, Alberto, et al. “A tutorial on synthetic aperture radar.” IEEE Geoscience and remote sensing magazine, (2013)

“The received echo signal data form a two-dimensional data matrix of complex samples, where each complex sample is given by its real and imaginary part, thus representing an amplitude and phase value.”

But I also read that in SNAP, to derive the amplitude and the phase from the i,q layers, one should apply these equations:
The amplitude = sqrt(i^2 + q^2)
The phase = arctan (i / q)
(What does Bands specify in SNAP toolbox?)

So i and q are not just amplitude and phase? In Sentinel -1 SLC there is already a Virtual intensity band. How is it derived?
Thank you as phase and amplitude have different units, they are expressed by two complex numbers, i and q. Together they allow to derive both amplitude and phase by these formulas.
Amplitude squared gives intensity. If you move your cursor over the intensity band in the Table of Contents (or open its properties) you can see its equation.