Do you have a name on this vector operation?

I get a vector by producing two single vectors. I'm putting them in the way of cosines and sinuses.
v3.x = v1.x * v2.x  v1.y * v2.y v3.y = v1.y * v2.x + v1.x * v2.y
Does this operation have a name in the context of the vectors?

https://ru.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BC%D0%BF%D0%BB%D0%B5%D0%BA%D1%81%D0%BD%D0%BE%D0%B5_%D1%87%D0%B8%D1%81%D0%BB%D0%BE#.D0.90.D0.BB.D0.B3.D0.B5.D0.B1.D1.80.D0.B0.D0.B8.D1.87.D0.B5.D1.81.D0.BA.D0.B0.D1.8F_.D1.84.D0.BE.D1.80.D0.BC.D0.B0 That's what it looks like.
(a + ib)(c + id) = (ac  bd) + i(bc + ad) ...где i  мнимая единица, для которой i^2 = 1
...which is https://ru.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BC%D0%BF%D0%BB%D0%B5%D0%BA%D1%81%D0%BD%D0%BE%D0%B5_%D1%87%D0%B8%D1%81%D0%BB%D0%BE#.D0.93.D0.B5.D0.BE.D0.BC.D0.B5.D1.82.D1.80.D0.B8.D1.87.D0.B5.D1.81.D0.BA.D0.B0.D1.8F_.D0.BC.D0.BE.D0.B4.D0.B5.D0.BB.D1.8C For vectors (in an integrated plane) the single length gives another vector a single length whose argument (the angle with Re+, the horizontal axis right) is the sum of the arguments of the constituents.
If they weren't the only ones, the length of the result would be the product of their length.