"normalize" a vector but conserve the "- sign"

I am confused at what you are trying to do.

If you give the Vector2(-3.4,4.0) and normalize it the new vector2 should be Vector2(-0.64764842,0.761939318) not Vector2(-1,1)

Normalize keeps the magnitude of the new Vector2 to 1, but preserves the direction.

What you describe here is not "normalizing". A normalized vector has an overall length / magnitude of 1.0. The vector (-1, 1) is not normalized. It has a length of "sqrt(2)" (about 1.41421)

Your original vector (-3.4, 4) has a length of about 5.248. When you actually normalize the vector the result would be approximately (-0.6476, 0.76194). This vector is normalized (has a length of 1.0 and does still preserve the direction)

I think you should be more clear about what you want to do.

Just for reference, this is how normalizing works:

 public static Vector2 Normalize(Vector3 aVec)
 {
     float len = $$anonymous$$athf.Sqrt(aVec.x*aVec.x + aVec.y*aVec.y);
     return new Vector2(aVec.x / len, aVec.y / len);
 }

So when you have a given vector "v" those lines do exactly the same:

 v = Normalize(v);
 
 v = v.normalized;