Dimensions of a Rug. Zachary wants to buy a rug for a room that is 12 ft wide and 15 ft long. He wants to leave a uniform strip of floor around the rug. He can afford to buy 108 ft2 of carpeting. What dimensions should the rug have?
Ch. 1 - Equations and Inequalities

Chapter 2, Problem 25
Perform each operation. Write answers in standard form. (5-11i)(5+11i)
Verified step by step guidance1
Recognize that the expression is a product of two complex conjugates: \((5 - 11i)(5 + 11i)\).
Recall the formula for the product of conjugates: \((a - bi)(a + bi) = a^2 + b^2\), where \(a = 5\) and \(b = 11\).
Calculate \(a^2\) which is \$5^2\( and \)b^2\( which is \)11^2$ separately.
Add the results from the previous step to get \(a^2 + b^2\).
Write the final answer in standard form \(x + yi\), noting that the imaginary part will be zero because the product of conjugates is a real number.

Verified video answer for a similar problem:
This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
1mWas this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Complex Numbers and Standard Form
Complex numbers are expressed in the form a + bi, where a is the real part and b is the imaginary part. The standard form means writing the answer explicitly as a sum of a real number and an imaginary number. Understanding this form is essential for correctly presenting the result of operations involving complex numbers.
Recommended video:
Multiplying Complex Numbers
Multiplication of Complex Numbers
To multiply complex numbers, use the distributive property (FOIL method) to expand the product. Multiply each term in the first complex number by each term in the second, remembering that i² = -1. This process combines like terms to simplify the expression.
Recommended video:
Multiplying Complex Numbers
Simplifying Using i² = -1
Since i is the imaginary unit, i² equals -1. This identity allows you to convert powers of i into real numbers, simplifying expressions involving complex numbers. Applying this rule is crucial when combining terms after multiplication.
Recommended video:
Powers of i
Related Practice
Textbook Question
106
views
Textbook Question
Perform each operation. Write answers in standard form. (-8+2i)(-1+i)
822
views
1
rank
Textbook Question
Solve each equation using the zero-factor property. 36x2 + 60x + 25 = 0
882
views
Textbook Question
Solve each inequality. Give the solution set in interval notation. -(2/3)x-(1/6)x+(2/3)(x+1)≤4/3
1964
views
Textbook Question
Solve each equation. -4(2x-6) +8x= 5x+24+x
879
views
Textbook Question
Solve each problem. See Example 2. At the 2008 Summer Olympics in Beijing, Usain Bolt set a new Olympic and world record in the 100-m dash with a time of 9.69 sec. If this pace could be maintained for an entire 26-mi marathon, what would his time be? How would this time compare to the fastest time for a marathon, which is 2 hr, 3 min, 23 sec, set in 2013? (Hint: 1 m ≈ 3.281 ft.) (Data from Sports Illustrated Almanac.)
682
views
