If a transformation t acts by rotating every point of the plane around the origin by $\pi/5$ clockwise and then proceeds to translate it by vector $v$ = $(1,2)$.
How do I describe this transformation by complex numbers? (Define the function t(z) so that the image of any point z is t(z) after this sequence of transformations.)
So do I go with... $t(z) = z + (1+2i)$?
A rotation is multiplying by a root of unity and in this case, it is $e^{-i\pi/5}$. A translation is addition, in this case, it is $1+2i$.
So putting everything together, we have $T(z)=z\cdot e^{-i\pi/5} +(1+2i)$.