Hello I wanted to know if someone can correct this exercise?

Exercice 17 Consider D as a line in the complex plane , passing through a point A with the complex number zo and having a directional vector U' with the complex number w. Let M be a point in the complex plane with the complex number z and M'with the complex number 2" is its image under the Orthogonal symmetry about the axis D. a / Demonstrate the identity w( 2'- 20) = w(2-Zo). b / Deduce from this that the complex expression of a symmetry is in the form ZI az+b where a is a complex number with a modules of 1. () show that the transformation CORResponding to the application Z Haz + b is a symmetry if and only if abtb= o d / Identify the transformation corresponding to the application Z IyaEth when the condition above is not satisfied