How do you simplify #(2-i)(3+2i)(1-4i)#?

1 Answer
sankarankalyanam
Jul 21, 2018

#color(cyan)(=> 12 - 31 i)#

Explanation:

Here are the steps required for Multiplying Complex Numbers:

#color(brown)("Step 1: Distribute (or FOIL) to remove the parenthesis."#

#color(purple)("Step 2 : Simplify the powers of i, specifically remember that i2 = –1."#
#color(gray)("Step 3 : Combine like terms, that is, combine real numbers with real numbers and imaginary numbers with imaginary numbers."#

#"Given : " (2 - i) * (3 + 2i) * (1 - 4i)#

#=> (6 + 4 i - 3 i - 2i^2) * (1 - 4i)#

#=> (6 + 4i - 3i + 2) * ( 1 - 4i)#

#=> (8 + i) * ( 1 - 4 i)#

#=> 8 - 32 i + 1 i - 4 i^2#

#=> 8 - 32 i + i + 4#

#color(cyan)(=> 12 - 31 i)#

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