Almost:

Lengths are usually reals, and in this case the diagram we can use assume that A is the origin wlog (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 out other length √2.

Squaring isn’t multiplication by complex conjugate, that’s just mapping a vector to a scalar (the complex | x | function).