Perform the indicated operation

(1 - 3i) (5 + 5i) (4 - 1i) =

70-60i

Step-by-step explanation:

(1 - 3i) (5 + 5i) (4 - 1i) =

taking the first two, before we do the last one

(1 - 3i) (5 + 5i)

1 (5+5i) - 3i (5+5i)

1 (5) + 1 (5i) - 3i (5) - 3i (5i)

5+5i-15i-15i²

from the miltiplication law, i² is - 1

5-10i-15i² = 5-10i-15 (-1) = 5-10i+15 = 5+15-10i = 20-10i

then multiply (20-10i) (4 - 1i)

20 (4 - 1i) - 10i (4 - 1i)

20 (4) - 20 (1i) - 10i (4) - 10i (-1i)

80-20i-40i+10i²

80-60i+10 (-1)

80-60i-10

80-10-60i

(1 - 3i) (5 + 5i) (4 - 1i) = 70-60i

(1 - 3i) (5 + 5i) (4 - 1i)

= (5 + 5i - 15i - 15i²) (4 - 1i)

= (5 - 10i - 15i²) (4 - 1i)

= 20 - 40i - 60i² - 5i + 10i² + 15i³

= 20 - 45i - 50i² + 15i³