Question

The invariant point of the transformation w=2 - (2/z) is​

Answer 1

Answer:

Step-by-step explanation:

           u = u(x, y)

           v = v(x, y)

represents a function that assigns to every number pair (x, y) another number pair (u, v). The number pairs (x, y) and (u, v) can be viewed as representing points in a plane and the system can be viewed as defining a point transformation that maps a point (x, y) in an xy-coordinate system into a point (u,v) in a uv-coordinate system. See Fig. 1. In the same way the system

           u = u(x, y, z)  

           v = v(x, y, z)

           w = w(x, y, z)  

 

represents a function that assigns to every number triple (x, y, z) another number triple (u, v, w). The number triples (x, y, z) and (u, v, w) can be viewed as representing points in three-dimensional space and the system can be viewed as defining a point transformation that maps a point (x, y, z) in an xyz-coordinate system into a point (u, v, w) in a uvw-coordinate system. Generalizing on this idea the system of equations

 

           u1 = u1(x1, x2, ... , xn)

           u2 = u2(x1, x2, ... , xn)

           .....

           um = um(x1, x2, ... , xn)

 

assigns a point (u1, u2, ... , um) in m-dimensional space to a point (x1, x2, ... , xn) in n-dimensional space. The domain is some specified point-set in n-dimensional space and the range is some point-set in m-dimensional space. It can be viewed as defining a point transformation from n-space into m-space.

 

Syn. mapping, point transformation, transformation

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Answer 2

Answer:

1 ± 2i

Step-by-step explanation:

Invariant points are given by

w = f(z) = z

⇒ $2-\frac{2}{z} = z$

⇒ $z^{2}-2z+2=0$

Solving for z by quadratic formula we get,

z = ( 2 ± 4i) / 2

z = 1 ± 2i