This is from an introductory complex analysis textbook:

Express the given composition of mappings as a linear mapping .

(A) rotation through , magnification by 2, and translation by

(B) magnification by 2, translation by , and rotation through

(C) translation by , rotation through , then magnification by 2

The results are all supposed to turn out the same. I get that in (A) the answer is , but how do you do translations first and then rotation/magnification?