Question

当实数m取何值时,复数z=(m²-3m+m²i)-［4+(5m+6)i］为实数?虚数?纯虚数?零?

Answer 1

解:z=(m²-3m-4)+(m²-5m-6)i=(m+1)(m-4)+(m+1)(m-6)i.?

z为实数(m+1)(m-6)=0m=-1或m=6;?

z为虚数 (m+1)(m-6)≠0m≠-1且m≠6;?

z为纯虚数 m=4;?

z为零 m=-1.