After reviewing the rectangular/polar coordinate conversions we started yesterday, we revisited the original composition of transformations we looked at on Monday, noting that the Dilation x1/2, Rotation 45°, and Translation up 4 corresponds to an iteration of the function Az+B, where

- A = [.5, 45°] = √(2)/4 + √(2)/4
*i* - B = (0, 4) = 4
*i*

Iterating this function allowed us to find that the coordinates of the attracting fixed point we identified earlier to be roughly positioned at (-2.605, 4.763) (or equivalent to the complex number -2.605+4.763*i*).

From there, we looked at a few problems from the back of the Complex Transformations Sheet, identifying again the specific geometric transformations that each complex linear function would produce and sketching the new location of a point that underwent that transformation. **Your homework**** is to finish the back of that sheet**

With the time we had left, we introduced a new piece of software: Complex Paint, a tool for more easily illustrating the transformations we have been identifying. We will work with this in more detail tomorrow.