Source: cirosantilli/norm-induced-by-the-complex-dot-product
= Norm induced by the complex dot product
{tag=Norm induced by an inner product}
Given:
$$
x = \sum_{k=1}^n a_k + b_k i \in \C^n, a_k, b_k \in \R
$$
the norm ends up being:
$$
|x| = \sqrt{\sum_{k=1}^n a_k^2 + b_k^2}
$$
E.g. in <\C^2>:
$$
|(2 + 3i, -1 + 5i)| = \sqrt{2^2 + 3^2 + (-1)^2 + 5^2} = \sqrt{4 + 9 + 1 + 25} = \sqrt{39}
$$