Question

已知復數Z=" a" + b i, ( a, b∈R)且a + b =" 25," (3 + 4i ) Z 是純虛數。
求Z的共軛復數？

Answer 1

 = 4－3 i 或=－4+3 i

解: (3 + 4 i ) Z =" (3" + 4 i ) ( a + b i ) =" (3" a－4 b) + ( 4 a + 3 b ) i 是純虛數
∴
∴b = a 代入a + b =" 25 " 得 a = ±4
∴當a = 4時,，b = 3，   當a = －4 時b = －3
∴Z =" 4" + 3 i 或Z =－4－3 i
∴ = 4－3 i 或=－4+3 i