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)

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 ...