Exercise 64 Page 183

We are asked to simplify the following expression. [(2+i)x^2-ix+5+i]-[(-3+4i)x^2+(5-5i)x-6] Notice that this is a difference of two quadratic expressions in x. a x^2+b x+c Let's collect like terms according to powers of x.

[(2+i) x^2-i x+5+i]-[(-3+4i) x^2+(5-5i) x-6]

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Remove parentheses

Distr

Distribute x^2 & x

[2 x^2+i x^2-i x+5+i]-[-3 x^2+4i x^2+5 x-5i x-6]

Distr

Distribute -1

[2 x^2+i x^2-i x+5+i]+3 x^2-4i x^2-5 x+5i x+6

RemovePar

Remove parentheses

2 x^2+i x^2-i x+5+i+3 x^2-4i x^2-5 x+5i x+6

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Simplify

CommutativePropAdd

Commutative Property of Addition

2 x^2+3 x^2+i x^2-4i x^2-5 x+5i x-i x+6+5+i

FactorOut

Factor out x^2 & x

(2+3+i-4i) x^2+(-5+5i-i) x+6+5+i

AddSubTerms

Add and subtract terms

(5-3i) x^2+(-5+4i) x+11+i

The simplification of the given expression is quadratic in x with complex coefficients. (5-3i) x^2+(-5+4i) x+(11+i)