Exercise 63 Page 183

We are asked to find the sum of the following two expressions. ix^2-(4+5i)x+7 3x^2+(2+6i)x-8i Notice that both of these expressions are quadratic in x. a x^2+b x+c Let's add the two expressions, and collect the terms corresponding to the same power of x to simplify.

(i x^2-(4+5i) x+7)+(3 x^2+(2+6i) x-8i)

▼

Simplify

RemovePar

Remove parentheses

i x^2-(4+5i) x+7+3 x^2+(2+6i) x-8i

Distr

Distribute x

i x^2-4 x-5i x+7+3 x^2+2 x+6i x-8i

CommutativePropAdd

Commutative Property of Addition

3 x^2+i x^2-4 x-5i x+2 x+6i x+7-8i

FactorOut

Factor out x^2

(3+i) x^2-4 x-5i x+2 x+6i x+7-8i

FactorOut

Factor out x

(3+i) x^2+(-4-5i+2+6i) x+7-8i

AddSubTerms

Add and subtract terms

(3+i) x^2+(-2+i) x+7-8i

The sum of the given expressions is quadratic in x with complex coefficients. (3+i) x^2+(-2+i) x+(7-8i)