當分母為 虛數數值不等於零的複數, 以共軛作擴分母
例子:
1/(2+3i) = 1/(2 + 3i) x (2 – 3i)/(2 – 3i)
= [1 x (2 + 3i)] / [ (2 + 3i) x (2 – 3i)]
= [2 + 3i] / [ 2×2 -2x3i + 2x3i – 3ix3i]
= [2 + 3i] / [ 4 + 0 – 9(i x i)]
= [2 + 3i] / [ 4 – 9x (-1)]
= [2 + 3i] / [ 4 + 9]
= 2/13 + (3/13) i
例子:
(3 + 2i) x (4 + 5i) = 3 x (4 + 5i) + 2i x (4 + 5i)
= 12 + 15i + 8i + 10(i x i)
= 12 + 23i + 10 x (-1)
= 12 + 23i – 10
= 2 + 23i
共軛 Conjugate Pair
實數部份相同, 虛數部份則正負號相反
例子1:
3 + 4i 的共軛 是 3 – 4i
例子2:
3 + 5i 的共軛 是 3 – 5i
例子3:
8 + 5i 的共軛 是 8 – 5i
實數與虛數單位i, i x i = -1
例子1:
3i x i = 3 x (i x i) = 3 x (-1) = -3
例子2:
(2i + 5) + 6i = 5 + (2i + 6i) = 5 + 8i
例子3:
(2i + 5) – 6i = 5 + (2i – 6i) = 5 – 4i