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

1 Answer
Mar 20, 2016

#(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#