Simplify the following expression (10-4i) (4-5i) (-15+20 I)

Step-by-step explanation:

(10-4i) (4-5i) (-15+20i)

(10-4i) (4-5i) = 10 * (4-5i) - 4i * (4-5i)

= 10*4 - 10*5i - 4i*4 + 4i*5i

= 40 - 50i - 16i + 20i² = 40 - 66i + 20*-1 {i² = -1}

= 40 - 66i - 20

= 20 - 66i

(20 - 66i) (-15 + 20i) = 20 * (-15 + 20i) - 66i * (-15 + 20i)

= - 300 - 400i + 990i - 1320i²

= - 300 - 400i + 990i - 1320 * (-1)

= - 300 - 400i + 990i + 1320

= 1020 + 590i