hi, at 11.11 you have said that first we have to take the absolute value of component and than square it. But on the contrary, does not we have to take first the product of it with its complex conjugation and then absolute value? for exp. v=((i-1),(i+1)) so ||v|| = root( |(i-1)(i+1)| + |(i+1)(i-1)| ) = root( |-1-1| + |-1-1| ) = root(4). Here how can i get the absolute value of (i+1) or in which sense i can evaluate it as positive or negative, since it lies in plane not in line, if C is thought as R*R.
I think in 11:11 should be root(abs(i^2)+abs(-1^2) then equal to root(2). for the should be then the u*u congi is always positive length squared.
What is the difference to 11:11?
hi, at 11.11 you have said that first we have to take the absolute value of component and than square it. But on the contrary, does not we have to take first the product of it with its complex conjugation and then absolute value?
for exp. v=((i-1),(i+1)) so ||v|| = root( |(i-1)(i+1)| + |(i+1)(i-1)| ) = root( |-1-1| + |-1-1| ) = root(4). Here how can i get the absolute value of (i+1) or in which sense i can evaluate it as positive or negative, since it lies in plane not in line, if C is thought as R*R.
The complex absolute value is defined in my other video series about complex numbers: tbsom.de/s/slc
Will you later be covering vector spaces over any field?
Yes, but first abstract vector spaces of R and C.