Let the contour C be the triangle with vertices (0,0), (2, 0), and (0, 2), oriented counterclockwise. Let f(x + y) = xy + i(x² - 2y). Determine Sc f(z) dz.

Let G(u, v) = (5u + v, 30u + 13v) be a map from the uv-plane to the xy-plane. Find the image of the line through the points (u, v) = (1, 1) and (u, v) = (1,–1) under G in slope-intercept form. (Express numbers in exact form. Use symbolic notation and fractions where needed.) equation:

Construct a linear map L(z) = az + b that will send the imaginary y-axis to the line v = - u

Find the distance from the point (-3,1,0) to the line d(t) = (1, 0, 2)t + (4, – 9, – 2) .