this post was submitted on 30 Oct 2024
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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 โ2.
Squaring isn't multiplication by complex conjugate, that's just mapping a vector to a scalar (the complex | x | function).