Evaluate dz/z-2 around (a) the circle |z − 21 =4, (b) the circle |z1|=5, (c) the square with vertices at 3 + 3i, -3 ± 3i.

Find the point (x,y) on the line y=x that is equidistant from the points (3,8) and (−10,−10)

Suppose you are climbing a hill whose shape is given by the equation z = 1600 – 0.005x² – 0.01y², where x, y, and z are measured in meters, and you are standing at a point with coordinates (60, 40, 1566). The positive x-axis points east and the positive y-axis points north. (a) If you walk due south, will you start to ascend or descend? ascend descend At what rate? vertical meters per horizontal meter (b) If you walk northwest, will you start to ascend or descend? ascend descend At what rate? (Round your answer to two decimal places.) vertical meters per horizontal meter (c) In which direction is the slope largest? What is the rate of ascent in that direction? vertical meters per horizontal meter At what angle above the horizontal does the path in that direction begin? (Round your answer to two decimal places.)

Find the point on the ellipse x² + 6y² + 3xy = 40 with the greatest x-coordinate. (Use decimal notation and fractions where needed. Give your answer as the coordinates of a point in the form (*,*).) (x, y) =