How do you simplify #(1-4i)(2+i)#?

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Answer 1 · 2018-04-07T02:54:02

#5-7i#

Keep in mind that #i^2=-1#, and proceed, multiplying this with a method resembling FOIL:

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

#1+i-8i-4i^2#

Combine the like terms in the middle.
#1-7i-4i^2#

#1-7i-(4*-1)=5-7i#

Answer 2 · 2018-04-07T02:56:58

#6-7i#

#(1-4i)(2+i) = 1times (2+i)-4i times (2+i)#
#qquad = 1 times 2+1 times i -4i times 2-4i times i#
#qquad = 2+i-8i-4i^2 = 2-7i+4 = 6-7i#