1. Let x = = [ x-[2] and y=[-12] (a) 3 points Are x and y orthogonal with respect to the dot product? Explain why or why not. (b) Are x and y orthogonal with respect to the following inner product? (x, y) = x¹ Ay Explain why or why not. where A = 3 -2 -2 5

Let C denote the rectangle with vertices (0, -2), (0, 2), (2,-2), and (2, 2), oriented counterclockwise. Find So COS TTZ 2² - 1 dz

Evaluate fe z sin(22) dz where C is the union of the lower-half of the unit circe in clockwise direction AND the directed line segment that joins the point (-1, 0) to the point (-3, 4).

Rewrite the following complex functions as real mappings: 3z Z 1 = = 1, I(2³) = 5, |z| = Rz + 2