∴{■(log_2 "(" m^2 "-" 3m"-" 3")" =0"," @log_2 "(" 3"-" m")" ≠0"," @m^2 "-" 3m"-" 3>0"," @3"-" m>0"," )┤∴m=-1.

答案-1

7已知 =(m2-5m-6)+(m2-2m-3)i(m∈R),则当m=　　　　时, 为实数;当m=　　　　时, 为纯虚数.

解析当 为实数时,由m2-2m-3=0,

　　得m=3或m=-1.

　　当 为纯虚数时,由{■(m^2 "-" 5m"-" 6=0"," @m^2 "-" 2m"-" 3≠0"," )┤得m=6.

答案3或-1　6

8若不等式m2-(m2-3m)i<(m2-4m+3)i+10成立,求实数m的值.

分析由于题目中两个复数能比较大小,故它们都是实数,由此列出关于m的方程组,求出m的值. 学 ]

解由题意,得{■(m^2 "-" 3m=0"," @m^2 "-" 4m+3=0"," @m^2<10"," )┤即{■(m=0"或" m=3"," @m=3"或" m=1"," @"|" m"|" <√10 "," )┤

　　故实数m的值为3.

9定义运算|■(a"　" b@c"　" d)|=ad-bc,如果(x+y)+(x+3)i=|■(3x+2y"　" i@"　-" y"　" 1)|,求实数x,y的值.

解由定义运算|■(a"　" b@c"　" d)|=ad-bc,

　　可得|■(3x+2y"　" i@"　-" y"　" 1)|=(3x+2y)+yi.

　　所以(x+y)+(x+3)i=(3x+2y)+yi.

　　由复数相等的充要条件得{■(x+y=3x+2y"," @x+3=y"," )┤

　　解得{■(x="-" 1"," @y=2"." )┤

能力提升 学

1已知集合M={1,2,(m2-3m-1)+(m2-5m-6)i},集合P={-1,3},M∩P={3},则实数m的值为(　　)

A.-1 B.-1或4

C.6 D.6或-1

解析∵M∩P={3},

∴(m2-3m-1)+(m2-5m-6)i=3.