In parts (a)–(c), express the given composition of mappings as a linear mapping f(z) = az...

In parts (a)–(c), express the given composition of mappings as a linear mapping f(z) = az + b.

(a) rotation through π/4, magnification by 2, and translation by 1 + i

(b) magnification by 2, translation by , and rotation through π/4

(c) translation by , rotation through π/4, then magnification by 2

(d) What do you notice about the linear mappings in (a)–(c)?