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

50+50i

Explanation:

(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

Answer 2

complex numbers multiplication is commutative.
so

given
= (2+i)(1+2i) * (3-i)(3+i) * (1-i)

|(2+i)(1+2i)| has 5 as its absolute value and geometrically thinking its argument is pi/2. so

(2+i)(i+2i) = 5i

and obviously

(3+i)(3-i) = 10

so the answer is

50i * (1-i) = 50 + 50i

maybe, I think...