define a map

**yellow4321** · January 27th 2008, 12:33 PM

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**ThePerfectHacker** · January 27th 2008, 01:01 PM

Originally Posted by yellow4321

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.

**yellow4321** · January 27th 2008, 02:11 PM

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**ThePerfectHacker** · January 27th 2008, 03:37 PM

Originally Posted by yellow4321

where r= reflection and t=translation

(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 $f(z) = \bar z$ is the reflection of a complex number through the x-axis. And $g(z) = z+1$ is a translation of a number by 1 unit to the right. Hence $f\circ g = \bar z + 1$ is a glide reflection.

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