How to calculate the length of a complex vector? Suppose I have a two-dimensional complex vector a, how can I prove that the square of its length is equal to the conjugate product of a and a? In other words, why is it not equal to the product of a and a itself? I know that the conjugate of a and a can guarantee that the product is positive, but why is the length calculated in this way?

Suppose a = x + Yi conjugate complex B (that sign cannot be typed) = x-yi
The length of a | a | = x ^ 2 + y ^ 2
The product of a and conjugate complex number = (x + Yi) * (x-yi) = x ^ 2 - (y ^ 2 * I ^ 2) = x ^ 2 - [y ^ 2 * (- 1)] = x ^ 2 + y ^ 2
It is proved that the two are equal

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