Question

How do you simplify `(3-i)(1+2i)(2+3i)`?

Answer 1

`(3-i)(1+2i)(2+3i) = -5+25i`

Explanation:

Multiply out one pair of numbers as a product of binomials, simplify using `i^2 = -1` and repeat with the remaining pair.

You can use FOIL if you find it helpful.

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

`=overbrace((3*1))^"First" + overbrace((3*2i))^"Outside" + overbrace((-i*1))^"Inside" + overbrace((-i * 2i))^"Last"`

`=3+6i-i-2i^2`

`=3+5i+2`

`=5+5i`

Similarly:

`(5+5i)(2+3i)=10+15i+10i-15=-5+25i`

So:

`(3-i)(1+2i)(2+3i) = -5+25i`