Originally Posted by **avito009** After googling I could see vector product and scalar product in Euclidean Space. |

You need to be careful with your terms. The vector product and scalar product of two vectors in Euclidean space are also commonly known as the

cross product and

dot product.

What you are trying to look at is if we have a scalar a belonging to the complex number system and a vector

**v** belonging to the "usual" vector space on the Euclidean plane, then can we multiply the two? If V is a vector space and $\displaystyle \textbf{v} \in V$ and $\displaystyle a \in \mathbb{C}$ then

**v'** = a

**v** implies that $\displaystyle \textbf{v}' \in V$ as well.

Note, though, that a scalar

*can* change the direction of a vector... If that scalar is a negative number then the direction points the other way.

-Dan