How do you evaluate #(x-3)(-20i^{2}-19ix+6x^{2})#?

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Answer 1 · 2018-04-29T14:10:06

#6x^3 - 19ix^2 - 18x^2 + 57ix + 20x - 60#

you can find the products of each term in the complex polynomial with #x-3# separately:

#-20i^2(x-3) = -20i^2x + 60i^2#

#-19ix(x-3) = -19ix^2+57ix#

#6x^2(x-3) = 6x^3-18x^2#

add them together:

#-20i^2x + 60i^2 - 19ix^2 + 57ix + 6x^3 - 18x^2#

sort in order of degree:

#6x^3 - 19ix^2 - 18x^2 - 20i^2x + 57ix + 60i^2#

you can then note that #i^2 = -1#, and then simplify further:

#6x^3 - 19ix^2 - 18x^2 + 20x + 57ix - 60#

and then sort again in order of degree:

#6x^3 - 19ix^2 - 18x^2 + 57ix + 20x - 60#