Question

Find the bilinear transformation that maps the points 0, -i, -1 into the points i, 1, 0. Which of the following options is correct?

a) w = t(1+z/1-z)
(b) w = i\left(\frac{1+z}{1-2z}
(c) w = i\left(\frac{1+2z}{1-3z}
(d) w = i\left(\frac{2+z}{3-z}

Answer 1

The correct answer option is (b) w = i(1+z)/(1-2z). The bilinear transformation is a mapping that transforms points in the complex plane. By substituting the given points into the formula, we find that the correct coefficients are a = i, b = 1, c = -2, and d = 1. Therefore, the correct bilinear transformation is w = i(1+z)/(1-2z).

Step-by-step explanation:

The correct answer option is (b) w = i\left(\frac{1+z}{1-2z}\right).

The bilinear transformation is a mapping which transforms points in the complex plane. In this case, we want to find the transformation that maps the points 0, -i, -1 to the points i, 1, 0.

We can use the formula w = \frac{az+b}{cz+d} to find the transformation. By substituting the given points into the formula, we can solve for the unknown coefficients a, b, c, and d. After substituting the given points, we find that the correct coefficients are a = i, b = 1, c = -2, and d = 1. Therefore, the correct bilinear transformation is w = i\left(\frac{1+z}{1-2z}\right).