Problem 14

Question

Find each product and write the result in standard form. $$ (8-4 i)(-3+9 i) $$

Step-by-Step Solution

Verified

Answer

The product of the complex numbers $ (8 - 4i) $ and $ (-3 + 9i) $ is $ 12 + 84i $.

1Step 1: Distribute

The first step involves using the distributive property to multiply each term in the first complex number with each term in the second complex number. This yields the equation: $ 8 \cdot (-3) + 8 \cdot 9i - 4i \cdot (-3) - 4i \cdot 9i $. After performing these multiplications, the expression simplifies to $ -24 + 72i + 12i - 36i^2 $.

2Step 2: Replace $ i^2 $

The term $ i^2 $ can be replaced with -1 (since $ i^2 = -1 $). So the expression becomes $ -24 + 72i + 12i + 36 $.

3Step 3: Combine Like Terms

Combine the real parts and the imaginary parts separately. This results in $ (-24 + 36) + (72i + 12i) $, which simplifies to $ 12 + 84i $.

Problem 14

Other exercises in this chapter

Problem 14

In $2000,$ the population of Greece was $10,600,000,$ with projections of a population decrease of $28,000$ people per year. In the same year, the populat

View solution

Problem 14

Solve and check each linear equation. $$5 x-(2 x+2)=x+(3 x-5)$$

View solution

Problem 14

Graph each equation in Exercises $13-28 .$ Let $x=-3,-2,-1,0$ $1,2,$ and 3. $$y=x^{2}+2$$

View solution

Problem 15

Solve each radical equation in Exercises 11–30. Check all proposed solutions. $$\sqrt{2 x+13}=x+7$$

View solution