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This feels wrong. I love it. (sopuli.xyz)

submitted 2 weeks ago by hydroptic@sopuli.xyz to c/science_memes@mander.xyz

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[-] ornery_chemist@mander.xyz 32 points 2 weeks ago

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 + - i^2^) = √(1 + 1) = √2. I could be totally off base here and could be confusing with something else...

[-] diaphanous@feddit.org 16 points 2 weeks ago

I think you're thinking of taking the absolute value squared, |z|^2 = z z*

[-] candybrie@lemmy.world 5 points 2 weeks ago

Considering we're trying to find lengths, shouldn't we be doing absolute value squared?

[-] HexesofVexes@lemmy.world 1 points 2 weeks ago* (last edited 2 weeks ago)

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).