rotation: z = re^iθ → re^i(θ + a) = (e^ia)z , k = (e^ia)
magnification: z → kz, k real
translation: z → z + k, k complex
example: z → (z + k1) → k2(z + k1) → k3[k2(z + k1)]
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?