Warning: Some posts on this platform may contain adult material intended for mature audiences only. Viewer discretion is advised. By clicking ‘Continue’, you confirm that you are 18 years or older and consent to viewing explicit content.
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…
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?
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).