Simplify the following product of complex numbers. (8 + i) • (4 – 3i)
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English
Identify the structure used in each of the sentences below. 1. The hamburger came from Hamburg, Germany, and the hot dog came from Frankfurt. simple compound complex compoundcomplex 2. The idea of placing meat on a bun, however, came from the United

Precalc
To which set(s) of numbers does the number sqrt 16 belong? Select all that apply. real numbers complex numbers*** rational numbers imaginary numbers*** irrational numbers I can only pick two, and that's what I think it is. Please check? Thanks

Math help Ms. Sue please
1. Name the subset(s) of real numbers to which the number zero belongs. You can choose more than one answer. Irrational numbers Integers Whole numbers Natural numbers 2. Write an algebraic expression for the word phrase: the quotient of r and 12. r * 12 r

Algebra 2
What is the maximum product of two numbers whose sum is 22? What numbers yield this product?

math
Please check my answers! Simplify the product. 7x(x+4) A. 7x^2+4 B. 7x^2+28x

math induction
prove the product of 4 consecutive integers is always divisible by 24 using the principles of math induction. Could anyone help me on this one? Thanks in advance! Sure For induction we want to prove some statement P for all the integers. We need: P(1) to

math
Algebra 1.) Use the distributive Property to simplify the expression . (1)(4  c) A. 4  c B. 4 + c C. 4 + c D.4  c 2.)Use the distributive Property to simplify the expression 4(2x  4) A.8x + 4 B.8x  4 C.8x  16 D.4x  16 3.) Use the distributive

English
Choose the term that describes the type of sentence shown. If you are in line early, you'll be sure to get the best tickets. A.) compoundcomplex B.) complex C.) compound D.) simple I think it is C? John was late to dinner and I was late to the movies. A.)

maths
the sum of N positive integers is 19. what is the maximum possible product of these N numbers? thx. Nice problem. Let's look at some cases 1. N=2 clearly our only logical choices are 9,10 for a product of 90 It should be obvious that the numbers should be

Algebra 2
What is the product of a complex conjugated? The product of complex conjugates is a difference of two squares it is always a real number. The product a complex conjugates may be written in standard form as a + bi where neither a nor b is zero. The product

high school (math)
Match the mathematical expression with its translation. 1. the product of two numbers 2. y divided by x 3. six less than a number is y 4. x subtracted from y 5. the sum of two numbers is six 6. x minus y 7. the sum of x and y 8. x divided by y 9. six times

math
the sum of two numbers exceeds their product by one. their differences is equal to their product less five . find the two numbers

math
1. What is the first step to evaluate this expression? 73 – 4 • 3 + 8 (1 point) exponent subtraction multiplication* addition 2. Simplify 2 + (5 × 4 + 3). (1 point) 31* 25 37 43 3. Which shows the product of a number n and 12? (1 point) n – 12 n

MATH HELP
What is the simplified form of the expression? Hint: Combine like terms 7m2 + 6.5n – 4n +2.5m2 – n A)9.5m2 + 1.5n B)4.5m2 + 1.5n C) 9.5m2 – 1.5n Which property is illustrated by the statement? 8 + 3.4 = 3.4 + 8 A)Associative Property of Addition B)

Math
Use the product property for radicals to simplify the following radical expressions as much as possible. Assume all variables represent positive numbers. Use sqrt(x) for √x and root(x)(y) for x√y. 3√750x^4y^7

Algebra 2 Help
1.) Solve for x. 2x(x  12) = 40 2.) Solve for x. 3x2 + 2x = 12  7x 3.) Simplify the expression. 8sqrt[63] 4.) Find the absolute value of the complex number. Abs Val [7 + 24i] 5.) Simplify the expression. [4  7i] + [2 + 3i] Thank you so much!! :)

PreCal
There exist two complex numbers c, say c1 and c2, so that 2 + 2i, 5 + i, and c form the vertices of an equilateral triangle. Find the product c1 c2. I need help

statistics
supposed that two balanced dice are rolled. let Y denote the product of the two numbers. use random variable notation to represent the event that the product of the two numbers is greater than 4 a {5,6} b {XY>4} c{Y>4} d P(Y>4)

Math
1) for any three consecutive numbers, what can you say about odd numbers and even numbers? Explain. 2 A)Mirari conjectures that, for any three consecutive numbers, one number would be divisible by 3. Do you think Mirari is correct? Explain. 2 B) Gia claims

math
Find the two numbers that multiply to the product number and add to the sum number of the following: a)Product 563033256; Sum 51895 b)Product 43481220; Sum 28429 c)Product 2545124358; Sum 105619 I tried xy = product and x+y = sum, but it didn't work

Algebra II
Simplify the complex fraction: x+(4x/y)/(7/3x) I know that the answer is 3x^2(y+4)/7y. I don't know how to get this answer. Can someone please help me walk through this and figure out how to simplify it? I would be so grateful.

Precal
The equation of the line joining the complex numbers 5 + 4i and 7 + 2i can be expressed in the form az + b*overline{z} = 38 for some complex numbers a and b. Find the product ab. Any help?

Math
The product (5+i)(5−i) is a real number, 26. What are the factors (5+i) and (5−i) called? imaginary units** complex numbers complex conjugates imaginary numbers My answer is A but im not sure if thats right

Math
Factor the polynomial as the product of factors that are irreducible over the real numbers. Then write the polynomial in completely factored form involving complex nonreal or imaginary numbers. x^4 + 20x^2 44=0

Math
One number is 10 less than twice a second number. Find a pair of such numbers so that their product is as small as possible. These two numbers are_ and _. (Use a comma to separate your numbers.) The smallest possible product is_. The number are NOT 5,15 or

Mathematics
The sum of two numbers exceeds their product by one.Their difference is equal to their product less five. Find the two numbers.

Algebra 2
Operations with complex numbers What is the product of complex conjugates? The product of complex conjugates is a sum of two squares and is always a real number. The product of complex conjugates may be written in standard form as a+bi where neither a nor

algebra 2
1.Simplify the difference. n^2  lOn+24 9 / n^2  13n + 42 — 7 A. n13/n7

math
1. What is the first step to evaluate this expression? 73 – 4 • 3 + 8 (1 point) exponent subtraction multiplication addition 2. Simplify 2 + (5 × 4 + 3). (1 point) 31 25 37 43 3. Which shows the product of a number n and 12? (1 point) n – 12 n over

Algebra 2
1.) Solve for x. 2x(x  12) = 40 2.) Solve for x. 3x2 + 2x = 12  7x 3.) Simplify the expression. 8sqrt[63] 4.) Find the absolute value of the complex number. Abs Val [7 + 24i] 5.) Simplify the expression. [4  7i] + [2 + 3i] Thank you so much!! :)

math
Simplify the following quotient of complex numbers into the form a + bi. 88i/1+2i

math
What is the product of the complex numbers (3i+4) and (3i+4)? I've forgotten how to do this...

Algebra
Multiply. x(6+2i)][x(62i)] Note that these expressions contain complex numbers. Simplify your answer as much as possible.

Algebra 2
Rewrite x^2+9 as a product using complex numbers and the polynomial identity below. a. (x+3)(x3) b. (x+3i)(x3i) c. (3x)(3i) d. (x+9i)(x9i) I'm not sure if it's b or d, if I'm on the right path. Please help? Thanks

Algebra
1.) Use the distributive Property to simplify the expression . (1)(4  c) A. 4  c B. 4 + c C. 4 + c D.4  c 2.)Use the distributive Property to simplify the expression 4(2x  4) A.8x + 4 B.8x  4 C.8x  16 D.4x  16 3.) Use the distributive Property to

Calculus
How is the product of a complex number and a real number represented on the coordinate plane? A)When 3 + 2i is multiplied by 3, the result is 9 + 6i. Graphically, this shows that the product is a scalar and a counterclockwise rotation of 90° of the

Algebra
28. Use the Distributive Property to simplify x(4x^2 + x + 4) Is it 4x^3 + x^2 + 4x? 42. To which set of numbers does 0 not belong? 46. Pi belongs to which group of real numbers? a. Odd numbers b. rational numbers c. irrational numbers C? 48. Can a number

Maths complex numbers
Find tan(3 theta) in terms of tan theta Use the formula tan (a + b) = (tan a + tan b)/[1  tan a tan b) in two steps. First, let a = b = theta and get a formula for tan (2 theta). tan (2 theta) = 2 tan theta/[(1  tan theta)^2] Then write down the equation

intermediate algebra
Simplify the following quotient of complex numbers into the form a+bi 1+8i  6+i

mathematics
A sequence of numbers begins with 1, 1, 1, 1, 1. Each new number is found by taking the product of the two preceding numbers. For instance the sixth number is the product of the fourth and fifth numbers. What is the sum of the first 2013 numbers?

maths
Find all complex numbers z satisfying the equation e 6 iz = 3i. Give your answer in Cartesian form, and indicate them on the complex plane.

calculus
can you please explain tep by step how to solve dividing complex numbers strictly using a graph, the complex plane. I know how to do it algebraically, but not graphically. thankyou

mathword problems with quadratics
I have 5 questions... 1) The sum of two numbers is 12. Their product is 36. Find the two numbers. 2) The sum of two numbers is 15. Their product is 100. Find the two numbers. 3) The sum of two numbers is 8. Their product is 12. Find the two numbers. 4)

math
Simplify the following product of complex numbers. (8 + i) • (4 – 3i)

precalculus
The equation of the line joining the complex numbers 5 + 4i and 7 + 2i can be expressed in the form az + b \overline{z} = 38 for some complex numbers a and b. Find the product ab. I can get the equation of the line by slope intercept but I don't know how

Algebra II
PLEASE HELPPPPPP What are the possible numbers of positive, negative, and complex zeros of f(x) = x4 + 3x3 − 2x2 + 1? (6 points) Positive: 2 or 0; negative: 2 or 0; complex: 4, 2, or 0 Positive: 2, or 0; negative: 4, 2 or 0; complex: 4, 2, or 0 Positive:

masterin quantum
Consider the left shift operator on the space of infinite sequences of complex numbers: L(z1,z2,…)=(z2,z3,…). Is L injective? Yes Yes  incorrect No Is L surjective? Yes Yes  correct No Find the eigenvalues and eigenvectors of L. Then complete the

Math
supposed that two balanced dice are rolled. let Y denote the product of the two numbers. use random variable notation to represent the event that the product of the two numbers is greater than 4 a {5,6} b {XY>4} c{Y>4} d P(Y>4)

Math
When factoring a trinomial that is in the format Ax^2 + Bx + C, the number that is represented by B should be viewed as the _____? a. product of two numbers b. the sum of two numbers c. square root of two numbers d. remainder of two numbers I believe it

Algebra II
I have some questions on my assignment, if you don't mind could you look over my answers. thanxs! Find all the numbers that must be excluded from the domain of the rational expression. x+8/x^216, my answer: x cant be 4 or 4 x3/x^2+11x+24, my answer: x

MATH
How do you write fractions in simplest form? for example I need explanation 48/66 Also I started on another one it states that I have to multiply. and I have to be sure to simplify each product 7/9 x 3/5 My answer: 21/45 I just don't know what goes after

Math  6th Grade
The sum of two decimal numbers is 5.3. Their difference is 1.7, and their product is 6.3. What are the two numbers? Does the product have anything to do with getting the answers?

Math
What is 2 + 2? = 4 What is 2 * 2? = 4 So, the sum and the product of these two numbers is the same. Are there other numbers that have this same property? Yes Determine all number pairs x and y such that the product of x and y and the sum of x and y are

Calculus
Score for Question 2: ___ of 40 points) For the polynomial (x)=x^55x^4+12x^324x^2+32x16 , answer the following questions. Show all of your work. How many zeros does the function have over the set of complex numbers? What is the maximum number of local

math
You can use the prime factorization of a number, written as the product of powers of prime numbers, to find the number of factors the number has. First, express the number as a product of powers of prime numbers; for example, 36=2 to power 2 3 to power 3

Math
Find all complex numbers $z$ such that $z^4 = 4.$ Note: All solutions should be expressed in the form $a+bi$, where $a$ and $b$ are real numbers.

MATHS!!!Please HELP..:'(
What is the sum of all integer values of n satisfying 1≤n≤100, such that (n^2)−1 is a product of exactly two distinct prime numbers? Details and assumptions The number 12=2×2×3 is the product of 3 (not necessarily distinct) prime numbers.

intermediate algebra
Simplify the following product of complex numbers (10+3i)*(2)

math
solve and simplify the answer completely by using pure imaginary numbers/complex numbers. 2x^2+3x+2=0

Math
simplify (8 – i) – (4 – i) using Complex Numbers

can someone please help me?
simplify the following expressions involving complex numbers. (3+2i)(7i) 10 + 3i how did you do that? can you show me this one and explain how this time? (3+2i)(7i) or even (32i)^2 you would do 3+2i=5i, then 7i=7i then 5i+7i=12i (3+2i)(7i) =

algebra
Can someone please help me with these problems? Please and thank you. 1)Solve the equation: (1/x)+[x/(x+2)]=1 2)Simplify the complex fraction: 3(3/4)  (1/2)(1/4) (1/x)+ [x/(x+2)] = 1 Convert left side to the sum of fractional terms with common

algebra2
simplify the following quotient of complex numbers into the form of a+bi 9+8i/1+2i

math b
last question finally simplify complex numbers: i^16/i^3

Algebra 2/Trig.
I forgot some stuff from my 7th grade algebra class about complex numbers...like what do you do with a problem like this 5+5i 3i divided by + divided by 2i 4+3i thanks.(divided by refers to dividing line in a fraction) In each case, RATIONALIZE the

Math
We have to simplify complex numbers and I was wondering whether I did these problems correctly. 1. 4i^22i^3 = 4+2i 2. (i)^3 = i 3. (the square root of a 2)^6= 8 4.1/(2i)^3 = i/8

Math
I am in the 5th grade and my homework tonight is about complex numbers. I have no idea how to do complex numbers, not to mention, I don't know what they are. Can you help me?

Precalculus
Let z and w be complex numbers such that 2z2=25, z+2w=5, and z+w=2. Find z. I first squared both equations and expressed the square of the magnitudes in terms of the complex numbers and its conjugates. Next, I summed the equations together and

Algebra
Simplify the product using the distributive property. (3p + 2)(5p  1) simplify the product (2y  5) (3y + 1) can someone help point me in the right direction, with this COVID19 going around i havent had much time for school, and now it started back up

Precalculus
Let z and w be complex numbers such that 2z  w = 25, z + 2w = 5, and z + w = 2. Find z. I need a little help with absolute values on complex numbers.

math
simplify the following expressions involving complex numbers. (3+2i)(7i) is i like x? and how would this work i know that you do this: (3+2i)(7+i) to get rid of the sign between the expressions. but then what?

math
simplify the following expressions involving complex numbers. (3+2i)(7i) is i like x? and how would this work i know that you do this: (3+2i)(7+i) to get rid of the sign between the expressions. but then what?

maths
two numbers are in a gp,twice the product of the 1st two numbers is 9times more than the product of the last two numbers.if the product of all the number is 9.find the gp.

Complex numbers  quadratic formula
Let a and b be real numbers. The complex number 4  5i is a root of the quadratic z^2 + (a + 8i) z + (39 + bi) = 0. What is the other root? I did a lot of work on hand and with wolfram alpha but it doesn't simplify itself easily at all....anyone have any

Math
"The conjugate of the sum of two complex numbers is equal to the sum of the conjugates of the two complex numbers." This is true right?

Math
simplify the complex fraction 4/x+5 +2 _________ 14/x+5 2 Once i multiply by the LCD i get 4+2(x+5)/142(x+5) however i can't see what i can do next to simplify can you explain.

mathcomplex numbers
Sketch the sets of complex numbers in the complex plane that satisfy the following: a) z1=2 b) z3i=2 c) z5+2i=2 I'm not sure, but are you supposed to rearrange the whole thing to z=a+bi? So, part b would be z=2+3i.

ALGEBRA!!
calculate P(i) for the following polynomial p(x)=x3+2x25x+8 Find  z  for each of the following complex numbers and represent them on a complex plane. a. z=34i b. v=512i c.u=7+24i d.w=9+40i e.p=1+3i f.t=2i g.n=4 h.m=0 i.s=(√3i)2

Abstract Algebra
Let H={a+bi a,b is a element R, a^2+b^2=1} be a subset of the non zero complex numbers C*. Prove that H

Quick english help
Please check & see if I classified these sentences as simple, complex, or compound correctly! 1. His tie is going to choke him unless we can get it off. (Is this a complex sentence?) 2. She laughed so hard until the teacher told her to stop. (Is this a

Algebra
1. Subtract and simplify 18/y8  18/8y 2. subtract simplify if possible v5/v  7v31/11v 3. Simplify by removing factors of 1 r^281/(r+9)^2 4. Divide and simplify v^216/25v+100 divided by v4/20 5. find all rational numbers for which the rational

Circuits and electronics applications3
In working with complex exponentials we need some simple rules and short cuts for doing the algebra. Remember that a complex number z is a vector in the 2dimensional plane. It has a length (also called "magnitude") z and an angle ∠(z) measured

drbob222, math ,algebra
can you explain to me the following problem , ms.sue and others are trying to help me but they are making me more confuse. Is there any short cuts to the following problem. Directions:multiply and write the answer in simplest form. 4/12 times 10/4 first,

Math SCREAMING for HELP
Use the quadratic formula to slove the equation. x^2x=7 This is what I have got so far and I do not think this is right: x=1(1)±√1^24(1)(7)/2(1) x=1±√14(7)/2 x=1±√21/2 x=1±21/2 and here I am lost! Use rational exponents to simplify.

math
You can use the prime factorization of a number, written as the product of powers of prime numbers, to find the number of factors the number has. First, express the number as a product of powers of prime numbers; for example, 36=2 to power 2 3 to power 3

Algebra
Find four consecutive natural numbers if you know that the product of the first two is 38 less than the product of the following two numbers.

college algebra
1. divide and simplify x^2+x56/x^11 / x7/2x+2 2. find the product in simplest from for x^2+x6/2x^2x3 * x^72x^6+4x^5/x^4+8x 3. perform the indicated operations and simplify: 2/3x +4/3x^2 y^4 6/2x^4 y^5 4. perform the indicated operation and simplify

Math
If in index notation there are variables and numbers and question says to simplify and give answer as positive index then Is 1/3^2a^2 is it correct after simplifying all negative indices Or should we make it as 1/9a^2 Can we leave as 3^2? Or both Answers

Algebra 2
When dealing with imaginary and complex numbers, are there 2 solutions? I.e.: x^2=4 x=2,2 For: x^2=4 x=2i or 2i ? (Is there a 2i and 2i, like for real numbers?)

chemistry
How to find moles given oxidation numbers and chemical formula? Trying to do my chemistry lab but i'm super duper stuck. please help me i'm gonna die. this is the part i'm stuck on: The overall charge on the complex, [Ni(en)(H2O)]^2+ * SO4^2 * H2O is

algebra
Help!! I am a homeschool mom who did horrible in Honors Algebra2. My daughter has done her work and I am stumped on two questions. Simplify. 6/x6+3x/x+51/(x6)(x+5) A) 3x+5/x^2x30 B) 3x^212x+29/x^2x30 C) 3x^2+6x+5/x^2x30 D) 3x^2+5/x6 Simplify

ALGEBRA
How many ordered triples of complex numbers(a,b,c) are there such that a^3b,b^3c,c^3a are rational numbers, and a^2(a^4+1)+b^2(b^4+1)+c^2(c^4+1)=2[{(a^3) b}+{(b^3)c}+{(c^3)a}]

math
How many ordered triples of complex numbers(a,b,c) are there such that a^3 b,b^3c,c^3a are rational numbers, and a^2(a^4+1)+b^2(b^4+1)+c^2(c^4+1)=2[{(a^3) b}+{(b^3)c}+{(c^3)a}]

math
How many ordered triples of complex numbers(a,b,c) are there such that a^3 b,b^3c,c^3a are rational numbers, and a^2(a^4+1)+b^2(b^4+1)+c^2(c^4+1)=2[{(a^3) b}+{(b^3)c}+{(c^3)a}]

ALGEBRA
How many ordered triples of complex numbers(a,b,c) are there such that a^3b,b^3c,c^3a are rational numbers, and a^2(a^4+1)+b^2(b^4+1)+c^2(c^4+1)=2[{(a^3) b}+{(b^3)c}+{(c^3)a}]

algebra, math
How many ordered triples of complex numbers(a,b,c) are there such that a^3 b,b^3c,c^3a are rational numbers, and a^2(a^4+1)+b^2(b^4+1)+c^2(c^4+1)=2[{(a^3) b}+{(b^3)c}+{(c^3)a}]

Chemistry
1. Can I2 react with Cyclohexane to form any product (without or without spectroscophic properties)? 2. Can I2 react with tbutyl or nbutyl alcohol to form any organic product? 3. What is the complex formed between I2 and tbutyl alcohol? Is this complex

LAL!
are these complex sentence. if it is complex, and are the subordinate clause right are these right? the subordinate clause are in capital letters 1IN THE 1950S the giants were the national league team from new york.( COMPLEX) 2 fans argued all the time

PreCalc
Find the maximum product of two numbers whose sum euqals 124. Let's call the numbers "x" and "y". Also, what are those two numbers?

PreCalculus
Three numbers whose sum is 15 are in an arithmetic progression. The product of the 1st two numbers is 2 more than the 3rd. Find the three numbers.