[1] z1 = -1+i = √2(cos 3π/4 + i sin 3π/4) z2 =√2(cos 5π/4 + i sin 5π/4)
[2] ウエ √√2(cos 3π/8 + i sin 3π/8), √√2(cos 11π/8 + i sin 9π/8)
オカ √√2(cos 5π/8 + i sin 5π/8), √√2(cos 13π/8 + i sin 13π/8)
キ w**4 + w**2 +2 =0 ク 0 ケ -2 コ -2
[3] S1*S1 = 1/4 x 2 x √2 x sin²3π/8 = 1√2 x 1/2(1-cos 3π/4) = (1+ 1/√2) / 2√2 = √2+1 / 4
S2*S2 = 1/4 x 2 x √2 x sin²5π/8 =1/4 x 2 x √2 x sin²3π/8 = S1*S1 ∴ S1/S2 = 1
[1] ア 4C2 = 6 イ 2/3 x 1/3 x 1/2 = 1/9 ウ 2/3 x 2/3 x 1/2 x 3/4 = 1/6
エ 1/3 x 1/3 x 1/2 x 3/4 = 1/24 2/3 x 1/3 x 1/2 x 3/4 = 1/12 1/9+1/6+1/24+1/12 = 29/72
[2] オ 1/3 x 2/3 x 1/2 = 1/9
BC 1/3 x 2/3 x 1/2 x 1/3 = 1/27 BD 1/3 x 2/3 x 1/2 x 1/2 = 1/18
CB 1/3 x 1/3 x 1/2 x 2/3 = 1/27 CD 1/3 x 1/3 x 1/2 x 1/2 = 1/36
DB 1/3 x 1/2 x 1/2 x 2/3 = 1/18 DC 1/3 x 1/2 x 1/2 x 1/3 = 1/36
カ (6+6+4+4+3+3)/108 = 13/54
[3] 1/2 pq + (1-p)q x 1/2 x 3/4 + p(1-q) x 1/2 x 3/4 + pq x 1/2 x 3/4 = 1/4 pq + 3/8 p + 3/8 q = 49/100
1/3 x (pq + 1/2p + 1/2 q) = 23/75 ∴ p= 4/5 q= 2/5
[1] a1 = 32 + 8 + 2 + 1 = 101011(2), a2 = 22 = 16 + 4 + 2 = 10110 (2), a3=44, a4=24, a8=0
キ: 7 (1-2-4-8-16-32-64) ク: 32 (2の倍数)
[2] 5 (1-4-16-64-256) , 4 (32の倍数)
[3] 三進法で１の位に１を足して繰り上げ、６桁以上を削る。11111(3)=27+9+3+1=40
