Question

practice concepts from previous topics. 1 rewrite each expression using multiplication. a (3 - 2i)(4 + 5i) b (7 - 6i)² 2 add or subtract the expressions given. a (4x² - 2x + 7) + (-8x² + 5x - 25) b (-9x² + 16x - 17) - (-12x² - 7 3 dilate each function by the given factor to create a new function of higher degre sketch the graph and then identify the zeros of the new function. a f(x) = (x + 3)(4x - 1) dilate by (x - 1). b f(x) = (x + 2)(x - 2) dilate by x.

Explanation:

Problem 1a:

Step1: Apply distributive property (FOIL)

$(3 - 2i)(4 + 5i)=3\times4 + 3\times5i-2i\times4-2i\times5i$

Step2: Simplify each term

$=12 + 15i-8i - 10i^2$

Step3: Recall $i^2 = -1$

$=12 + 7i-10\times(-1)$

Step4: Simplify further

$=12 + 7i + 10=22 + 7i$

Step1: Expand the square

$(7 - 6i)^2=(7 - 6i)(7 - 6i)$

Step2: Apply distributive property (FOIL)

$=7\times7-7\times6i-6i\times7 + 36i^2$

Step3: Simplify each term

$=49-42i-42i + 36i^2$

Step4: Recall $i^2=-1$

$=49-84i + 36\times(-1)$

Step5: Simplify further

$=49-84i-36 = 13-84i$

Step1: Remove parentheses

$(4x^2-2x + 7)+(-8x^2 + 5x-25)=4x^2-2x + 7-8x^2 + 5x-25$

Step2: Combine like terms

$=(4x^2-8x^2)+(-2x + 5x)+(7-25)$

Step3: Simplify each group

$=-4x^2 + 3x-18$

Answer:

$22 + 7i$

Problem 1b: