4) Let ƒz = dƒ/əz and ƒz = 0ƒ/əz. Recall ƒ = u + iv, the notation f is used for the complex conjugate function u – iv. (d) The Jacobian of ƒ, viewed as a map U → R², is defined by Jƒ = det(Dƒ). Show that Jƒ = |f₂|² − |fz|². In particular, if ƒ ≤ O(U), then Jƒ = |ƒ'|².

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Below are six functions, as well as six contour maps. Determine which function matches each contour map. Which contour map matches f(x, y) = vx? ? Which contour map matches f(x, y) = Vx2 + y2? ? Which contour map matches f(x, y) = x² – y? ? Which contour map matches f(x, y) = 6 – 2x – 3y? ? Which contour map matches f(x, y) = 1 – |x| – |y|? ? Which contour map matches f(x, y) = 4 – x² – y2? ? А B D F