Can I use a term "module" as an alternative for a term "absolute value"? For example, could this phrase be used:
"We need to raise the module of the amplitude to the second degree"
for this expression:
$p = |a|^2$
($a$ in this expression can be a real or complex number)
The correct term in English is modulus, the absolute value of a real or complex number.
Module is a generalization of vector spaces over rings.
In French, Italian, Spanish, and Portuguese, the same word (module, modulo, módulo) is used for both concepts.