Do the following complex number computations: a) (451 b) Let z = Compute z] and Zz 2+2 3+i3 1-i3 6-12i Use the Separation of Variables technique and solve the following ODES: a) xy' + 2x = y b) xy = xy + y (Hint: follow Example 1.3.2 on page 10 and set v = c) x + y - xyy' = 0 (Hint: follow Example 1.3.2 on page 10 and set v =) d) xy' = (x-y) + x (Hint: follow Example 1.3.2 on page 10 and set v = x - y) Show that each of the following paper is exact and find a solution: a) (2+x)y + 2xy-0 b) x +3y2y' = 0 c) sin 2x y' + 2y cos 2x = 0 * d) ex(y' + x) = 0