分からない問題はここに書いてね453

g(z) = e^(-z) -1 +z = [k=2,∞] (-z)^k /k!,

|g(z)| = |Σ[k=2,∞] (-z)^k /k! | ≦ Σ[k=2,∞] |z|^2 /k! ≦ |z|^2 Σ[k=2,∞] 1/k! = (e-2)|z|^2,

(左辺) = |(1+z)(1-z+g(z))-1| = | -zz + (1+z)g(z)| ≦ |z|^2 + |1+z||g(z)| ≦ |z|^2 + 2(e-2)|z|^2 = (2e-3)|z|^2,