Question

已知復(fù)數(shù)z1=

3

a+2

+(a2-3)i，z2=2+(3a+1)i，（I是虛數(shù)單位）．若復(fù)數(shù)z₁-z₂在復(fù)平面上對(duì)應(yīng)點(diǎn)落在第一象限，求實(shí)數(shù)a的取值范圍．

Answer 1

∵復(fù)數(shù)z1=

3

a+2

+(a2-3)i，z2=2+(3a+1)i，
∴z₁-z₂ =

3

a+2

-2+(a2-3a-4)i，又其對(duì)應(yīng)點(diǎn)落在第一象限
∴

3 a+2 -2＞0 a2-3a-4＞0

解得-2＜a＜-1
實(shí)數(shù)a的取值范圍是-2＜a＜-1