Isn’t the squaring actually multiplication by the complex conjugate when working in the complex plane? i.e., √((1 - 0 i) (1 + 0 i) + (0 - i) (0 + i)) = √(1 + - i2) = √(1 + 1) = √2. I could be totally off base here and could be confusing with something else…
Lengths are usually reals, and in this case the diagram suggests we can assume that A is the origin wlog (and the sides are badly drawn vectors without a direction)
Next we convert the vectors into lengths using the abs function (root of conjugate multiplication). This gives us lengths of 1 for both.
Finally, we can just use a Euclidean metric to get our other length √2.
Squaring isn’t multiplication by complex conjugate, that’s just mapping a vector to a scalar (the complex | x | function).
Isn’t the squaring actually multiplication by the complex conjugate when working in the complex plane? i.e., √((1 - 0 i) (1 + 0 i) + (0 - i) (0 + i)) = √(1 + - i2) = √(1 + 1) = √2. I could be totally off base here and could be confusing with something else…
Almost:
Lengths are usually reals, and in this case the diagram suggests we can assume that A is the origin wlog (and the sides are badly drawn vectors without a direction)
Next we convert the vectors into lengths using the abs function (root of conjugate multiplication). This gives us lengths of 1 for both.
Finally, we can just use a Euclidean metric to get our other length √2.
Squaring isn’t multiplication by complex conjugate, that’s just mapping a vector to a scalar (the complex | x | function).
I think you’re thinking of taking the absolute value squared, |z|^2 = z z*
Considering we’re trying to find lengths, shouldn’t we be doing absolute value squared?