Given equation x = 6 + i, w = -1 + 5i and z = 4 - 8i, determine each of the following in the form of a + bi

i) 2x + 4z

ii) w x z

i) 28 - 30i

ii) 36 + 28i

Step-by-step explanation:

i) x = 6 + i ⇒2x = 2(6 + i) = 12 + 2i

z = 4 - 8i ⇒ 4z = 4(4 - 8i) = 16 - 32i

2x + 4z = (12 + 2i) + (16 - 32i) = 28 - 30i

ii) w = -1 + 5i and z = 4 - 8i

w × z = (-1 + 5i)(4 - 8i) = -4 + 8i + 20i - 40⇒collect like terms

w × z = -4 + 28i - 40

∵

∴w × z = -4 + 28i - 40(-1) = -4 + 28i + 40 = 36 + 28i