What is the complex number C for the transformation T?

[avyunker]

The transformation T maps the plane onto itself by multiplication by a complex number. That is, there is a complex number C=a+ib such that for any point P(x,y), T(P) is the point corresponding to the complex number C⋅P. For a particular complex number C the transformation T takes the smaller house in the diagram to the larger one. The point A=(14,1) ( the upper left corner of the window) on the smaller house is taken to the point T(A)=(34,-112) on the larger house.

The complex number C=?

The small house is rotated ? degrees counterclockwise and expanded by a factor of ?

 

[Prove It]

The transformation T maps the plane onto itself by multiplication by a complex number. That is, there is a complex number C=a+ib such that for any point P(x,y), T(P) is the point corresponding to the complex number C⋅P. For a particular complex number C the transformation T takes the smaller house in the diagram to the larger one. The point A=(14,1) ( the upper left corner of the window) on the smaller house is taken to the point T(A)=(34,-112) on the larger house.

The complex number C=?

The small house is rotated ? degrees counterclockwise and expanded by a factor of ?

You need to work out a complex number (C = a + i b) such that (a + i b)(14 + i) = 34 - 112i.