5 Consider two complex variables w u iv and z x iy and the map given by w 2 For contours u constant in the w plane draw the contours to which they map in the 2 plane Repeat for contours constant in the w plane Show that the two sets of contours in the z plane are orthogonal to each other That is just as the contours for u constant and constant are perpendicular to each other everywhere they intersect so for the corresponding contours in the z plane For this reason we refer to this mapping function as a conformal map Conformal maps have many applications in science and engineering