this question has been bugging me:
how could i define a map f:Complex--->Complex (complex plane)
that is a glide reflection
i have ideas but struggling to put show as a map?
Hint: What is a glide reflection? It is a composition of a rotation and a reflection.
(t o r) perhaps but when i have it for the complex plane would i say r=reflection in some line x=3 perhaps, and translation by i or something?
Note the function $\displaystyle f(z) = \bar z$ is the reflection of a complex number through the x-axis. And $\displaystyle g(z) = z+1$ is a translation of a number by 1 unit to the right. Hence $\displaystyle f\circ g = \bar z + 1$ is a glide reflection.