(a) Prove that the composition of two translations T1(z) = z + b1, b1 ≠ 0, and T2(z) = z + b2, b2 ≠ 0, is a translation or the identity mapping. Does the order of composition matter?
(b) Prove that the composition of two rotations R1(z) = a1z, |a1| = 1, and R2(z) = a2z, |a2| = 1, is a rotation or the identity mapping. Does the order of composition matter?
(c) Prove that the composition of two magnifications M1(z) = a1z, a1 > 0, and M2(z) = a2z, a2 > 0, is a magnification or the identity mapping. Does the order of composition matter?
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