I have read from my algebra book that the product of two complex numbers is still a complex number: (a+bi)(c+di)= (ac-db)+(bc +ad)i I was thinking that since complex numbers can be used to represent vectors, the product of two vectors should still be a vector. But I have also read from my physics book that there are two ways to multiply vectors, which are the dot product and the cross product.The dot product is the product of two parallel vectors and results into a scalar, while the cross product is the product of two perpendicular vectors. Why should these products be defined differently? Using complex no.s, two vectors whether parallel or not should still yield a product which is still a vector. Are these dot and cross products different from ordinary complex number multiplication? If so, when do we use the ordinary complex no. or vector multiplication? Am i missing anything? What math topics should i read? Please reply, i'm really getting confused. Any help will be greatly appreciated!!