Question

(高二数学题)设复数z=lg(m^2-2m-2)+(m^2+3m+2)i,试求m取何值时 (1)z是实数;(2)z是纯虚

Answer 1

(1)虚部为0：m^2+3m+2=0 m=-1,m=-2

(2)实部为0：lg(m^2-2m-2) m^2-2m-2=1 m^2-2m-3=0 m=-1（舍）m=3

（3）实部虚部均大于0：

m^2+3m+2>0 m>-1或 m0 m^2-2m-2>1 m^2-2m-3>0 m>3 m