Using complex plane (x,y), and fact that z=re^i(theta):
a) Draw all points (a,b) which satisfy a/b = 3/4.
b) Provided any two points (a,b) and (c,d) let f((a,b),(c,d)) = |ad-bc|. Is f the function? Is f invertible?
c) Let (a,b) + (c,d) = (ad+bc, bd). Explain this operation as the function, algebraically and geometrically. ("+" in this case is vector addition, that is operation we speak of when adding two points)
d)Let (a,b) x (c,d) = (ac-bd, bc+ad). Explain this operation as the function, algebraically and geometrically.
(Note: "x" in this case is vector multiplication, that is operation we speak of when multiply two points)
Draw the picture to help explain the answers.