Question

已知复数z=k²-3k+(k²-5k+6)i(k∈R),且z＜0,则k=_________________.

Answer 1

思路解析:认真审题,把握“z＜0”,说明“z是实数且小于0”,然后具体求解.

∵z＜0,则z∈R.

故虚部k²-5k+6=0,∴(k-2)(k-3)=0.∴k=2或k=3.但k=3时,z=0,不合题意,故舍去,故k=2.

答案:2