The question of the day.
From
Richard Hachel@21:1/5 to
All on Tue Mar 4 20:36:18 2025
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.
--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)
From
Richard Hachel@21:1/5 to
All on Tue Mar 4 20:33:11 2025
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.
--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)