实数m取什么值时复数z=(m^2+5m+6)+(m^2-2m-15)i是

Question

实数m取什么值时 复数z=(m^2+5m+6)+(m^2-2m-15)i是

Answer 1

(1)
(m^2+5m+6)+(m^2-2m-15)i = 2 - 12i
m^2+5m+6 = 2 且 m^2-2m-15 = -12.
m^2+5m+4 = 0 且 m^2-2m-3 = 0.
(m+1)(m+4)= 0 且 (m+1)(m-3)= 0.
(m=-1 或m=-4) 且 (m=-1 或 m=-3)
m=-1.
(2)
(m^2+5m+6)+(m^2-2m-15)i = 12-6i
m^2+5m+6 = 12 且 m^2-2m-15 = -6.
请自己算或另外提问
(3)
(m^2+5m+6)+(m^2-2m-15)i 在x轴上方
m^2-2m-15 > 0
请自己算或另外提问