解答
化简 (3+i)26
解答
33554432+335544323i
求解步骤
(3+i)26
使用二项式定理: (a+b)n=i=0∑n(in)a(n−i)bia=3,b=i
=i=0∑26(i26)(3)(26−i)ii
展开求和
=0!(26−0)!26!(3)26i0+1!(26−1)!26!(3)25i1+2!(26−2)!26!(3)24i2+3!(26−3)!26!(3)23i3+4!(26−4)!26!(3)22i4+5!(26−5)!26!(3)21i5+6!(26−6)!26!(3)20i6+7!(26−7)!26!(3)19i7+8!(26−8)!26!(3)18i8+9!(26−9)!26!(3)17i9+10!(26−10)!26!(3)16i10+11!(26−11)!26!(3)15i11+12!(26−12)!26!(3)14i12+13!(26−13)!26!(3)13i13+14!(26−14)!26!(3)12i14+15!(26−15)!26!(3)11i15+16!(26−16)!26!(3)10i16+17!(26−17)!26!(3)9i17+18!(26−18)!26!(3)8i18+19!(26−19)!26!(3)7i19+20!(26−20)!26!(3)6i20+21!(26−21)!26!(3)5i21+22!(26−22)!26!(3)4i22+23!(26−23)!26!(3)3i23+24!(26−24)!26!(3)2i24+25!(26−25)!26!(3)1i25+26!(26−26)!26!(3)0i26
化简 0!(26−0)!26!(3)26i0:1594323
化简 1!(26−1)!26!(3)25i1:138174663i
化简 2!(26−2)!26!(3)24i2:172718325i2
化简 3!(26−3)!26!(3)23i3:4605822003i3
化简 4!(26−4)!26!(3)22i4:2648347650i4
化简 5!(26−5)!26!(3)21i5:38842432203i5
化简 6!(26−6)!26!(3)20i6:13594851270i6
化简 7!(26−7)!26!(3)19i7:129474774003i7
化简 8!(26−8)!26!(3)18i8:30750258825i8
化简 9!(26−9)!26!(3)17i9:205001725503i9
化简 10!(26−10)!26!(3)16i10:34850293335i10
化简 11!(26−11)!26!(3)15i11:168971119203i11
化简 12!(26−12)!26!(3)14i12:4790016001.01172E19i12
化简 13!(26−13)!26!(3)13i13:62270208003⋅4.72135E19i13
化简 14!(26−14)!26!(3)12i14:7040463300i14
化简 15!(26−15)!26!(3)11i15:18774568803i15
化简 16!(26−16)!26!(3)10i16:1290751605i16
化简 17!(26−17)!26!(3)9i17:2530885503i17
化简 18!(26−18)!26!(3)8i18:126544275i18
化简 19!(26−19)!26!(3)7i19:177606003i19
化简 20!(26−20)!26!(3)6i20:6216210i20
化简 21!(26−21)!26!(3)5i21:5920203i21
化简 22!(26−22)!26!(3)4i22:134550i22
化简 23!(26−23)!26!(3)3i23:78003i23
化简 24!(26−24)!26!(3)2i24:975i24
化简 25!(26−25)!26!(3)1i25:263i25
化简 26!(26−26)!26!(3)0i26:i26
=1594323+138174663i+172718325i2+4605822003i3+2648347650i4+38842432203i5+13594851270i6+129474774003i7+30750258825i8+205001725503i9+34850293335i10+168971119203i11+4790016001.01172E19i12+62270208003⋅4.72135E19i13+7040463300i14+18774568803i15+1290751605i16+2530885503i17+126544275i18+177606003i19+6216210i20+5920203i21+134550i22+78003i23+975i24+263i25+i26
化简 1594323+138174663i+172718325i2+4605822003i3+2648347650i4+38842432203i5+13594851270i6+129474774003i7+30750258825i8+205001725503i9+34850293335i10+168971119203i11+4790016001.01172E19i12+62270208003⋅4.72135E19i13+7040463300i14+18774568803i15+1290751605i16+2530885503i17+126544275i18+177606003i19+6216210i20+5920203i21+134550i22+78003i23+975i24+263i25+i26:335544323i+33554432
=335544323i+33554432
Rewrite in standard complex form: 33554432+335544323i
=33554432+335544323i