# Question on a linear algebra formula for **inner product**

I am currently studying linear algebra, specifically the orthogonality of a set of vectors. I learnt that the inner product of the 2 vectors in the field $$mathbb {C}$$ can be expressed by the sum of multiplication of the one’s counterpart with another’s conjugated one.

$$ = sum a_i.bar bi$$

This formula can apply to a set of $$mathbb {R}$$ too. My question is why in the field $$mathbb{C}$$ we need to use the conjugated vector instead of the normal one.