Recall the following trigonometric identities:
(a) cos(θ1+θ2)=cosθ1cosθ2−sinθ1sinθ2;
(b) sin(θ1+θ2)=cosθ1sinθ2+cosθ2sinθ1.
Use these identities to show (using Wessel's analogy for the norm and angular displacement discussed in Section 1.1.4) that the ordered-pair definition for the product of two vectors must agree with Equation (1.10) of the text. In other words, show that it must be the case that, if z1=(x1,y1) and z2=(x2,y2), then z1z2=(x1x2−y1y2,x1y2+x2y1).