# Question: use the taylor series formula for the exponential function to...

###### Question details

- Use the Taylor series formula for the exponential function to show that
- Define and show that the map is a reflection about the x-axis.
- Show that the Euclidean length of a vector is given by
- Show that the map does not change the length of vectors.
- Explain why this map is a rotation by angle . Is it clockwise or anticlockwise?
- Explain why (where is a fixed complex number) is a translation.
- Discuss how to write a glide transformation in the complex plane.