MHB What is the complex number C for the transformation T?

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The transformation T maps points in the plane by multiplying them with a complex number C, expressed as C = a + ib. For the point A = (14, 1), the transformation yields T(A) = (34, -112), leading to the equation (a + ib)(14 + i) = 34 - 112i. The discussion emphasizes determining the values of a and b that satisfy this equation, which involves understanding the effects of rotation and scaling on the smaller house to achieve the larger one. The transformation involves both a counterclockwise rotation and an expansion factor, although these specifics are not provided. Ultimately, the goal is to find the complex number C that accurately represents the transformation.
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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 ?
 
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avyunker said:
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.
 
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