(1) ア γ-α / β-α = k とすると、(k-1)α + γ = kβ k =(3+√3)/(1-i) = (3+√3)(1+i) /2 ∴∠A=45
イ γ-β / α-β = m とすると、mα - γ = (1-m)β m =-(2+√3+i)/(1-i) = -(1+√3+(3+√3)i) /2 = (1+√3)(-1-√3i)/2 ∴∠B=120
ウ AB:AC = |β-α| / |γ-α| = 1/|k| = 2 : (3+√3)√2 = √2 : 3+√3
エ β-α = 2 60°回転 = cos π/3 + i sin π/3 = 1/2 + √3/2i 1+√3i + 1+i = 2+(1+√3)i
オ 直線AC: y=x ∴(1+√3) + 2i
(2) カ {2x1 + 3(n-3) x 1/2 + (n-3)(n-4)/2 x 1/2 x 1/2} / {n(n-1)/2} = n^2-n+2/2n(n-1)
キ {1 x (n-3) x 1/2 + (n-3)(n-4)/2 x 1/2 x 1/2} / {n(n-1)/2} = (n-3)n/4n(n-1) = (n-3)/4(n-1)
ク PB(C) = P(B∩C)/P(B) = {(n-3)(n-4)/2 x 1/2 x 1/2} / {1x(n-3)x 1/2+(n-3)(n-4)/2 x 1/2 x 1/2} = (n-3)(n-4)/n(n-3) = (n-4)/n
ケ PB(D) = P(B∩D)/P(D) ={1 x (n-3) x 1/2} / {1 x (n-3) x 1/2 + (n-3)(n-4)/2 x 1/2 x 1/2} = 4(n-3)/n(n-3) = 4/n
コ n = 8
