# complex numbers!

12,585 results

math-complex numbers
Sketch the sets of complex numbers in the complex plane that satisfy the following: a) |z-1|=2 b) |z-3i|=2 c) |z-5+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.

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?

Pre-cal
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?

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 (Complex Numbers)
Let a,b,c be complex numbers satisfying a+b+c=abc=1 and (ab+bc+ac)/3=(1/a^2)+(1/b^2)+(1c^2) The sum of absolute values of all possible ab+bc+ac can be written as (√n)/m, where n and m are positive coprime integers. What is n+m?

Complex Numbers
Let z and w be complex numbers such that |z| = |w| = 1, and zw is not equal to -1. Prove that (z + w)/(zw + 1) is a real number.

Complex Numbers
Let z and w be complex numbers such that |z| = |w| = 1, and zw is not equal to -1. Prove that (z + w)/(zw + 1) is a real number.

Complex Numbers
The system of equations |z - 2 - 2i| = \sqrt{23}, |z - 8 - 5i| = \sqrt{38} has two solutions z1 and z2 in complex numbers. Find (z1 + z2)/2. Im really just plain old confused. Could anyone help me out?

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: 2 or 0; negative: 2 ...

Complex numbers
Prove algebraically that |w+z| is less than or equal to |w|+|z| for any complex numbers w and z, where || is the magnitude. After letting w = a+bi and z = c + di and doing some plugging in etc. I got that ac-bd <= b^2 + sqrt (a^2+b^2)(c^2+d^2) + d^2 But is my proof complete...

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 help to offer? Thanks

Calculus--complex numbers

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?

complex numbers

complex numbers

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 for tan (2 theta + ...

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

Pre-calculus
Let z and w be complex numbers such that |2z-2|=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 attempted to solve for |...

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 to do this in the ...

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<C* under complex multiplication using the one-step subgroup test. Also describe the elements of H geometrically.

ALGEBRA!!
calculate P(i) for the following polynomial p(x)=x3+2x2-5x+8 Find | z | for each of the following complex numbers and represent them on a complex plane. a. z=-3-4i b. v=5-12i c.u=7+24i d.w=-9+40i e.p=1+3i f.t=-2i g.n=4 h.m=0 i.s=(√3-i)2

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 <text> Yes</text> - incorrect No Is L surjective? Yes <text> Yes</text> - correct No Find the eigenvalues and ...

math-complex numbers
If z = -3+4i, determine the following related complex numbers. a)vector z b)3(vector z) c) 1/(vector z) d) |z| e) |vector z| f) (vector z)/(|z|^2)

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?)

algebra, math
How many ordered triples of complex numbers(a,b,c) are there such that a^3- b,b^3-c,c^3-a 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^3-b,b^3-c,c^3-a 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^3-b,b^3-c,c^3-a 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^3-c,c^3-a 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^3-c,c^3-a 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
solve and simplify the answer completely by using pure imaginary numbers/complex numbers. 2x^2+3x+2=0

algebra2-imaginary numbers
You can add or subtract complex numbers by treating the i as a variable and combining like terms. I am having a lot of trouble figuring out these equations with imaginary numbers. 1. (3+2i)+(7-i)= 2.(1-6i)+(2-i)= 3. (2+i)-(3+i)= 4.(4+i)-(2-i)= Can someone please walk me ...

Roots, complex numbers
I want to solve z^5=-1 But all the examples I've seen use positive numbers. The -1 is throwing me off somewhat. Most of the examples I've worked with would be solved using the polar form I.e Z^5(cos5+i sin5)=1(cospi +i sinpi) But as I said negative numbers I'm finding confusing.

maths-complex numbers
by using the substitution w = z^3, find all the solutions to z^6 - 8z^3 +25 = 0 in complex numbers, and describe them in polar form, using @(theta) to denote the angle satisfying tan@ = 3/4 ( note simply leave @ as it is, don't calculate it). i got up to z^3 = 4+3i and 4-3i ...

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 compound-complex 2. The idea of placing meat on a bun, however, came from the United States. simple compound ...

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.) compound-complex B.) complex C.) compound D.) simple I think it is C? John was late to dinner and I was late to the movies. A.) simple B.) complex C...

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 zero; the charge on ...

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 complex sentence?) 3. ...

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 denominators. [(x+2) + x...

Complex Number Proof
Prove: If Z and W are complex numbers, then the conjugate of (Z+W) is equal to the conjugate of Z plus the conjugate of W. My thought is that this is kind of like the distributive property, but I'm not sure. It doesn't help that I haven't written a proof in over 10 years. Help...

If you fail to plan, you plan to fail. simple complex compound <----My choice compound-complex I was thinking about meeting Susan for dinner and then we could go shopping. compound simple complex <----My choice compound-complex Strawberries and bananas are my two ...

Math
I Don't Know What Is This Subject Called In English But It's About Complex Numbers it says 25 = 16 - 9 i^2 = (4 ± 3i) But My Teacher Says 25 = 25 - 0 i^2 = (5 ± 0i) I Think My Teacher Is Wrong , The Result Is 25 But There Will Not Be Complex Number Because ( 0i = 0) So Is My...

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

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

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 3-i divided by + divided by 2-i 4+3i thanks.(divided by refers to dividing line in a fraction) In each case, RATIONALIZE the denominator. Here is the ...

complex numbers
1) 4b-5t(-a-3)i=7-8i 2) (7+4i) - (l+2i) 3) (3+2i) (-2+4i)

Find the independent clauses and the dependent clauses.Write wether it is complex or compound-complex 1)Mr and Mrs Johnson play golf(ind) when the weather is warm.(dep)complex 2)What I would like is a vacation. independent,complex 3)Alicia works at the daycare center that is ...

Trigonometry
complex numbers

Math
Complex numbers 5i+7i x i

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 1-IN THE 1950S the giants were the national league team from new york.( COMPLEX) 2- fans argued all the time about WHO WAS THE ...

english
Write whether a sentence is simple, compound, complex, or compound-complex. 1-Mrs. Huang planned a party for Kim because she was graduating from high school. Complex 2=She invited Lisa,Elena,and Enrique to the party. Simple 3-Mr. Huang thought that kim's friends should come to...

complex numbers
find the values of x and y x+5i=y+yi

math b
divide complex numbers: 2+3-3i^3/1-i

Math
complex numbers: Evaluate z=(-j 3/4)^-j^3/4

Math
Dividing complex numbers 4-2i/3+1

English
When you are looking at a work by Monet, stand back at least fifteen or twenty feet. simple, compound, complex, compound-complex complex

English
Are these sentences compound, complex, or compound complex? Volunteer helped clear roads so that supplies could get to villages that needed them. Complex..

English
In the following sentence are they compound, complex, or compound complex All girls were taught spinning when they were quite young, and they also learned weaving. I think compound complex While housewives were at the marketplace, they met at the public fountain, and young ...

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

Math
Factor over {complex numbers} 9x^2 + 49

Precal
Prove algebraically that |w+z|<=|w|+|z| for any complex numbers w and z.

Math
Dividing complex numbers 7-13i/2i

math real and complex numbers lesson
(7,-9)+(3,5)

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

Trig/Precalc
The system of equations: |z-2-2i|=sqrt(23), |z-8-5i|=sqrt(38) has two solutions z_1 and z_2 in complex numbers. Find (z_1+z_2)/2. My first instinct on this problem was to square each equation given that the square of the magnitude of a complex number is much easier to deal ...

precalculus, complex numbers
Let $\omega$ be a complex number such that $\omega^7 = 1$ and $\omega \neq 1$. Let $\alpha = \omega + \omega^2 + \omega^4$ and $\beta = \omega^3 + \omega^5 + \omega^6$. Then $\alpha$ and $\beta$ are roots of the quadratic $x^2 + px + q = 0$ for some integers $p$ and $q$. ...

Calculus
two complex numbers Z and W are related by the formula W=(Z+1)/(1-Z) what is W if Z=1.5i? thanks for the help!

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

algebra
x^2+225 ..factor over complex numbers?

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

maths
compplex numbers multiplying complex and not: 3*(6-j8) also, 3+(6-J8)

math
For what real values of x and y are the numbers -3+i^2y and x^2+y+4i are conjugate complex

Algebra
Find all complex numbers such that z^2=2i. Thank you!

English
As it happens, you're right and I'm wrong. Tell if compound, complex, simple, compound-complex complex

Chemistry
8-hydroxyquinoline (Q) can complex and precipitate many metals. A mixture of the aluminium and magnesium complexes weighed 1.0843g (MW=459.43; 312.61). When ignited, the mixture decomposed and left a residue of Al203 (MW 101.96) and MgO (MW 40.304) weighing 0.1344g. What is ...

algebra
x^2+225 ... factor expression over the complex numbers?

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

division of complex numbers
(1-2i)/(2+3i) Do I multiply both the numerator and denominator by 2+3i?

Algebra 2
More About Complex Numbers Find the reciprocal. -1-i 2i

Math
Find all solutions for the complex numbers: a) z^4 = 9i -46 b) 8*sqrt3 / z^4 +8 =+i

Algebra
Find all complex numbers $z$ such that $|z|^2-2\bar z+iz=2i.$

Math
Complex Numbers please helpppppp and show solutions 1.) (3-7i) + (-1-2i) 2.) (4-5i) - (2-3i) 3.) (7-5i) + (6+9i) 4.) 2+3i/3-5i

English
Choose the term that best describes the underline term. 1. The toy "that Fido loves to chew" is made by hand. a. noun clause b. direct clause c. adverb clause d. adjective clause** Choose the term that describes the sentence shown. 1. If you fail to plan, you plan to fail. a. ...

Math
Use the quadratic formula to solve the equation. x² - x = -2 Type an exact answer, using radicals as needed. Express complex numbers in terms of i. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)

calculus
find the modulus and the argument of the following complex numbers: 15-4i and a-ai where a is greater than 0

math
Simplify the following quotient of complex numbers into the form a + bi. -8-8i/1+2i

algebra
Find the exact solutions to the quadratic equation in the complex numbers. (x-13)²=-36

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

Math
Let z and w be complex numbers such that |z| = |w| = 1, and zw is not equal to -1. Prove that (z + w)/(zw + 1) is a real number.

Precalculus
Let z and w be complex numbers such that |z| = |w| = 1, and zw is not equal to -1. Prove that (z + w)/(zw + 1) is a real number.

Algebra 2
Complex numbers are written in the form a + bi. What does i represent? -1 0 1 sqrt-1 **my choice

English
Is this sentence compound, complex, or compound complex? Charity groups distributed food and safe drinking water, and they handed out sleeping bags and mosquito nets, which were needed in the tropical climate. Is this compound complex?

English
Please check my work. Identify whether each sentence is complex, an exclamation, declarative, or interrogative. 1. Tim likes soup, so Mary bought tomatoes. Complex 2. Oh no! Exclamation 3. Do you want to play in the Garden? Interrogative 4. In the story, the author told how ...

English
Please check my work. Identify whether each sentence is complex, an exclamation, declarative, or interrogative. 1. Tim likes soup, so Mary bought tomatoes. ----- Complex 2. Oh no! ----- Exclamation 3. Do you want to play in the Garden? ----- Interrogative 4. In the story, the ...

Algebra II
Find the exact solutions to the quadratic equation in the complex numbers. (x-13)²=-36 HELP ME PLEASE!

Algebra II

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

maths (complex numbers)
if b is a real number satisfying b^4 + 1/(b^4) = 6, find the value of :- (b + i/b)^16 where i = sqrt of -1

maths
Find the number of different ordered quadruples (a,b,c,d) of complex numbers such that a^2=1 b^3=1 c^4=1 d^6=1 a+b+c+d=0

Complex numbers
If f(x) is a polynomial with real coefficients such that f(4+3i)=31+16i, then f(4−3i)=a+bi. What is the value of a+b

Math
Find the real and imaginary parts of the following complex numbers: (i) 1.5e^jπ/4 (ii) je^1.2 + j^2 e

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