The question of the day.

Friends of mathematical poetry, good evening.
The question of the day is: what is the modulus of a complex number?
Mathematicians are unable to answer.
So they say, and it is true, that |z|=sqrt(a²+b²)
But do they know how to define this in words?
Doctor Hachel tells us that it is the square root of the real part
of its square.
We still need to know the formula for the product of two complexes, which we pose badly, by distorting (I do not know why, its real part).
The correct equation is:
z1+z2=aa'+bb'+i(ab'+a'b) because we must not do i²=-1 at this point of conversions, but rather i²=1 because it is not the same i multiplied by itself.
So here we have z²=(a+ib)² and therefore Z=a²+b²+i(2ab)
We see immediately, if we are good mathematicians,
that the given definition is perfectly exact.
The modulus of a complex is the square root of the real part of its square.
Thank you for your attention.
R.H.