m2?3m?3??1 4．15 log2(m?3m?3)?2log2(m?3)?1?0,log2(m?3)22m2?3m?31?,m??15,而m?3,m??15
(m?3)2235．125 z?z?z?(2?i)?22?(5)6?125
21?i100501?i1001?i50?,z?z?1?()?()?1 1?i2222i502i2550252 ?()?()?1?i?i?1?i?i?1?i
222320007．1000?1000i 记S?i?2i?3i?L?2000i
2342000?2000i2001 iS?i?2i?3i?L?1999ii(1?i2000)23420002001(1?i)S?i?i?i?i?L?i?2000i??2000i2001??2000i
1?i?2000iS??1000?1000i
1?i6．i z?三、解答题
1．解：设z?a?bi,(a,b?R)，由z?1得a2?b2?1；
(3?4i)gz?(3?4i)(a?bi)?3a?4b?(4a?3b)i是纯虚数，则3a?4b?0
44??a?a?????43?a2?b2?1??55?43??,或?，z??i,或??i ?5555??b?3?b??3?3a?4b?0??55??2．解：设z?a?bi,(a,b?R)，而z?1?3i?z,即a2?b2?1?3i?a?bi?0
??a2?b2?a?1?0?a??4??,z??4?3i 则?b?3???b?3?0(1?i)2(3?4i)22i(?7?24i)24?7i???3?4i
2z2(?4?3i)4?i（数学选修2-2）第三章 复数 [综合训练B组]
一、选择题
1．B z1?a?bi,z2?c?di,(a,b,c,d?R),z1z2?z1z2?(a?bi)(c?di)?(a?bi)(c?di) ?2ac?2bd?R 2．B mm?X?(bi)???2??2????b?(b?R,且b?0)
2(?1?3i)3?2?i?1?3i3(?2?i)(1?2i)?1?3i3135i3．D ??()??()()? 6(1?i)1?2i2i52i5 ?i?i?2i
1?3i134．C z?3i?3zi?1?0,z????i??，z?z2????2??1
221?3i3?3i3i?3135．A z????i
22?23i236．C z1?z2422?2(z1?z2)?z1?z2?3,z1?z2?3
22227．B ????1?????1?0
8．C 二、填空题
1．5 2．
83
3．1?i 4．2?i 5．0 6．二 7．1?i 8．?1 9．?6 10．?2 32
数学选修2-2练习题及答案
