How do you multiply #(2+ i ) ( 1+ 2i ) #?

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Answer 1 · 2017-07-22T15:15:15

#5i#

You perform elementary operations involving imaginary numbers the same way as you would with all real numbers.

Use the F.O.I.L. method:

#(2+i)(1+2i) = 2 + 4i + 1i + 2i^2#

Combine like terms:

#= 2 + 5i + 2i^2#

Know that #i^2 = -1# (because #sqrt(-1) = i#):

#= 2 + 5i + 2(-1)#

#= 2 + 5i - 2#

#= color(blue)(5i#

Answer 2 · 2017-07-22T15:43:05

#5i#

#"expand the factors using FOIL"#

#•color(white)(x)i^2=(sqrt(-1))^2=-1#

#rArr(2+i)(1+2i)#

#=2+4i+i+2i^2=2+5i-2#

#=5i#