Exercise 2-1 The Joukowsky transformation w that maps circles into airfoil shapes f(z) is an important transformation (a) Compute the inverse of the Joukowsky transformation (b) Show that the circles |z- map into ellipses. What happens at -1? (c) Use MATLAB to map the circle centered at (-0.15, 0.25) and passing through the point z = 1 through f. (Hint: The new shape should be inside the rectangle [-1.25,1.25] x [-0.5,0.5].)