Determine and sketch the equations in the w-plane into which the equations [z] = 1 and |z-] = 3 are mapped under the transformation w= (2-2)/(2z-1).
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Solved in 4 steps with 2 images
- Find the kernel of the linear transformation T:R4R4, T(x1,x2,x3,x4)=(x1x2,x2x1,0,x3+x4).Sketch the image of the triangle with vertices (0, 0), (1, 0), and (0, 1) under the specified transformation.T is a reflection in the x-axis.Find the bilinear transformation that maps the point (0,1,π=∞) in z-plane onto the point (-1,-2,-i)in the w-plane
- Find the bilinear transformation whose fixed points are 1,i and maps 0 to -1.Sketch the image of the rectangle with vertices at (0, 0), (1, 0), (1, 2), and (0, 2) under the specified transformation.T is a reflection in the line y = x.Find the bilinear transformation which transform the points (∞,i,0) in the z-plane into the points (0,i,∞) in the w-plane
- Find the linear fractional transformation that maps (1, 0, i) to (1, 0, 1+i).Sketch the image of the rectangle with vertices at (0, 0), (1, 0), (1, 2), and (0, 2) under the specified transformation.T is the contraction represented by T(x, y) = (x/3, y).Sketch the image of the rectangle with vertices at (0, 0), (1, 0), (1, 2), and (0, 2) under the specified transformation.T is the contraction represented by T(x, y) = (x, y/2).
- Find the image of any point on x^2+y^2=4 under the transformation (x,y)-->(1/2x,1/2y).Sketch the image of the rectangle with vertices at (0, 0), (1, 0), (1, 2), and (0, 2) under the specified transformation.T is the expansion represented by T(x, y) = (2x, y).Sketch the image of a unit square [a square with vertices at (0, 0), (1, 0), (1, 1), and (0, 1)] under the specified transformation. T is a reflection in the line y = −x.