Bi-linear transformation 2

MODEL university questions on bi-linear transformation

1. Bilinear Transformation

2. Find the bilinear transformation which maps the points z = 0, - i , -1 into w= i , 1,0. Soln : Given z 1 = 0, z 2 = - i , z 3 = -1 and w 1 = i , w 2 = 1, w 3 = 0. The bilinear transformation is got by using the relation =  

3. which is the required transformation.  

4. Find the bilinear transformation which maps the points - i , 0, I into the points -1, i , 1 respectively. Into what curve the y-axis is transformed to this transformation? Soln : Using the relation we get the bilinear transformation. Here z 1 = - i , z 2 = 0, z 3 = i and w 1 = -1, w 2 = i , w 3 = 1.  

5. Therefore the required transformation is (since