Question

Perform the indicated multiplication below. Reduce terms and simplify. Include all of the necessary steps and calculations in your final answer.

(2 + i)(3 - i)(1 + 2i)(1 - i)(3 + i)

Answer 1

(2 + i)(3 - i)(1 + 2i)(1 - i)(3 + i)

(6-2i+3i-i^2)

(6+i+1)

(7+i)(1 + 2i)(1 - i)(3 + i)

(7+14i+i+2i^2)

(7+15i-2)

(5+15i)(1 - i)(3 + i)

(5-5i+15i-15i^2)

(5+10i+15)

(20+10i)(3 + i)

60+20i+30i+10i^2

60+50i-10

50+50i

Explanation:

Answer 2

Start by expanding the first two brackets

(2+i)(3-i)

Multiply 2x3=6, then 2x I = 2i, then i x 3= 3i, then i x i= i2( i squared)
so it will be written as 6+2i+3i+i2( squared)

from here you can see that 2i and 3i can be added together to make 5i
so, 6+5i+i2(squared)

Then you bring in the third bracket from the question.
(6+5i+i2)(3+i)

6 x 3=18
6 x i= 6i
5i x 3=15i
5i x i=5i2(squared)
2x3=6
2x i= 2i
so you get 18+6i+15i+5i2(squared)+6+21
6i and 15i can be added together
18, 6 and 21 can be added together

so, 21i+5i2(squared)+45