In the complex plane referred to a direct orthonormal system (0; ü; ö),consider the points A and B
such that: ZA = 1 and zg = i.
Let h be the homothecy with center A and ratio k = -2.
Let r be the rotation with center B and angle a =5.
1) Write the complex form of h and of r.
2) Consider the transformation S = hor.
a) Determine the nature of
S.
b) Write the complex form of S then deduce the affix of its center 2. 3) Consider the transformation R = Soh-1
a) Prove that R is a rotation whose angle is to be determined. b) Write the complex form of R then deduce the affix of its center 2'.
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