Complex number Definition and 438 Threads

Express in the form a+ib: (i+1)(i+2)(i+3)..(i+n) I can handle problems like i^n, but this one has been giving me issues.

let be n and integer and 'i' the imaginary unit is then true that n^{ \frac{2i\pi n}{log}} =1 i believe that is true

Homework Statement I could not type it here, so i made a screenshot and posted it below. Homework Equations it's about complex numbers undergraduate level. I'm currently doing Euler's formula and De Moivre's theorem, although I'm not sure that the solution lies there. The Attempt at...

Homework Statement (a) Suppose the segment connecting (a,b) to (0,0) has length r_{1} and forms an angle \theta_{1} with the positive side of the x-axis. Suppose the segment connecting (c,d) to (0,0) has a length r_{2} and forms an angle \theta_{2} with the positive side of the x-axis. Now...

Hi! I was presented with this problem: Let z +\neq -1 be a complex number with |z|=1. Show that \frac{z-1}{z+1} is an imaginary number. I am getting nowhere with the algebra, but i did notiec one thing: let z=1+0b and the equation says \frac{z-1}{z+1} = \frac{0}{2} = 0, which is...

how to solve sqrt(-8.3)sqrt(1 - i8)? i try to solve it.. but got the wrong answer.. sqrt(-8.3)sqrt(1 - i8) = sqrt[(8.3i^2)(1 - 8i)] = sqrt (8.3i^2 - 66.4i) = 2.88i + 8.15 the answer should be.. 5.41 + i6.13

why electromagnetic waves are represented by complex numbers?

In a complex number sum, I have encountered a minute difficulty in understanding a step: \left|(cos\theta-1)+i.sin\theta\right| = \sqrt{}(cos\theta-1)^2+sin^2\theta Now my question is, how did the 'i' got eliminated from the second step? Now, i equals \sqrt{}-1, so when squared, there...

Homework Statement In Griffiths' Introduction to Quantum Mechanics problem 2.22 as well as 6.7, I used substitution to complete an integral. The original integral had limits from negative infinity to positive infinity. For my substitution, I had a complex constant term added to the original...

Homework Statement For z complex: a.) is z\sqrt{2} a multi-valued function, if so how many values does it have? b.) Claim: z\sqrt{2}=e\sqrt{2}ln(z)=e\sqrt{2}eln(z)=ze\sqrt{2} Since \sqrt{2} has 2 values, z\sqrt{2} is 2 valued. Is this correct? If not, correct it. Homework...

Read the post first, then look at the graphs - https://picasaweb.google.com/104328106431858306974/Jun232011?authkey=Gv1sRgCIe1gv_A_bT__wE#5621389108478505394" Well this is the question...and I don't understand it very well : Suppose you know that x raised to the fifth power is 1. What can you...

I have solved part a, I just have no idea how to go about doing part b. If anybody could point me in the right direction, that would be greatly appreciated! Homework Statement a. Express z = \frac{1 + \sqrt{3}i}{-2 -2i} in the form rcis\theta b. What is the smallest positive integer n...

When is it true that \arg\left(z_1 z_2\right) = \arg(z_1) + \arg(z_2) ?

Hey guys, Just having a bit of trouble with inequalities. Homework Statement Sketch all complex numbers 'z' which satisfy the given condition: |z + i + 1| \leq |z - i| Homework Equations --- The Attempt at a Solution z + i + 1\leq z - i z + 2i + 1\leq z 2i + 1\leq...

Homework Statement Let R be a set of real numbers derived from rational numbers. And, let R* be a set consisting of all ordered pairs of the form (x,0) where x is an element of R. For a complex number z = (a,b) = a+ib, I've learned that the absolute value of z is the number...

Homework Statement Determine whether the indicated operations of addition and multiplication are defined (closed) on the set, and give a ring structure. If a ring is formed, state whether the ring is commutative, whether it has unity, and whether it is a field: The set of all pure...

divide complex number by conjugate. 1+3(sqrt-1)/ 2+(sqrt-1) The answer that i get is (5i/5)+1. Is this correct?

I think I got it

I have been doing some homework on synthetic division today. Most of it is pretty straight forward, until I got to a problem with complex number I was able to solve the first problem (x^3 – 3x^2 + x – 3) / (x-i) By using +i for the ‘synthetic divisor constant’ (sorry don’t know the proper...

Homework Statement Two alternating voltages are given by: V1= 12 sin 200pi t V2= 18 sin 200pi t + pi / 3 i) Plot each wave form on the same axis for one complete cycle ii) Add both together and plot the resultant waveform on the same axis iii) Using complex numbers, confirm ii)...

The problem is that I need to convert: \sqrt{27} + 3i From the form (a+bi) to Re^{i\theta}. I have no clue what to do with this. I do know the following: e^{i\pi}=cos(\theta)+sin(\theta)i=-1 But I don't see how that's helpful. This is the first of several problems.

find the integral int(1/z)dz along r for the curve: square with corners 1+i, -1+i, -1-i, 1-i traversed clockwise and anti-clockwise Homework Equations i know that clockwise will be the -(int) of the anticlockwise The Attempt at a Solution the first line = (1-2t)+i it's derivative...

Homework Statement I have no problem using DeMoivre's Theorem to find nth roots of a complex number. However, I really don't know what this is accomplishing. Usually the book I use explains the concept behind a certain type of problem, but in this case, there is nothing. I can easily get...

Complex number question (i think :) ) Homework Statement Solve the following equations in C : (a) z^2 + 3z + 2 = 0 The Attempt at a Solution I thought i should solve the quadratic for z, (z+1)(z+2)=0 and then somehow say that: 1=x+iy I don't really understand how to go...

Homework Statement The question is located here http://i51.tinypic.com/2cge9mt.jpg Homework Equations My a value is -3 my b value is -3sqrt(2) my c value is -2.4 The Attempt at a Solution 1) ln(-3 - 3 sqrt(2) i) = Ln |-3 - 3 sqrt(2) i| + i arg(-3 - 3 sqrt(2) i) = ln...

Homework Statement The question is located here http://i51.tinypic.com/nex2q1.jpg Homework Equations The value I have been given for a) is 5 The value I have been given for b) is 5PI/6 The Attempt at a Solution Note that e^(a + bi) = e^a e^(bi) = e^a (cos b + i sin b). (e^a is...

Homework Statement Solve the equation \overline{y} (y - 2) = 2\overline{y} + 15 - 8i for complex number y Homework Equations \overline{y}y = a2 + b2 The Attempt at a Solution a2+b2+8i-4ib-15=0 a2+b(b-4i)+8i-15=0 Pretty clueless where to go from here? Or if I've even gone in...

Homework Statement Under the section of complex number, i faced 2 questions which i couldn't answer... Here they go... -Show that x=1-2i is a root of the equation x3-3x2+7x-5=0. Hence, find all the roots of the equation. -Express...

hi, while trying to study complex analysis, i have a few problems. i already know that in complex number system, it's impossible for any order relation to exist. but i was confused to this fact when i saw the proof of triangle inequality. ; Let z,w be complex numbers. Then, triangle...

I have two complex numbers, let's call them A and B. A=2exp[-ikz], and B=2iexp[-ikz]. I have to figure out the angle of these two numbers, and I am just completely drawing a blank on B. I know that the angle of A is just -kz, but I can't remember how to figure it out for part B. I can't remember...

The question is to express (1- i tanx) / (1+ i tanx) in polar form. First, multiple the whole fraction by cosx. It becomes (cosx - i sin x) / (cosx + i sin x). We can find the modulus and argument easily by using the fact that "if z1=r cis a, z2=r cis b , then z1 / z2 = r1/r2 [cos(a-b) + i sin...

Homework Statement I'm pretty sure that I just don't fully understand these problems so I think I just need help getting pushed in the right direction here. Anyways, here's the problem I'm on. Evaluate and give your answer in Cartesian Coordinates...

Homework Statement (5e^(j*a))(3 + j*b) = -25 Find real numbers a and b satisfying the preceding equation. There are two different answer sets for {a,b} so find both of them. Homework Equations e^(j*a) = cos(a) + j*sin(a) The Attempt at a Solution I converted it to get 5*sqrt(9...

How do you get the exponential form of 1/j? I saw a problem that says it's e^(-j*pi/2) but I have no idea where that came from. Also, if you have a complex number, z, how do you find it's magnitude? For example, e^(j*pi*t - pi/2). In my book when they square the the magnitude of a complex...

Homework Statement My prof was saying today that the modulus of a complex number isn't the absolute value. The problem is the following: Graph the set of points satisfying the following equation(s): |z-1+i|=1 The Attempt at a Solution Can I not just say that z = -i or z = 2-i...

Homework Statement let z , w be complex nos. such that z + i ( conjugate of w ) = 0 and zw = pi . Then find arg z.. Homework Equations The Attempt at a Solution well i m unable to understand wat is meant by zw=pi...

Homework Statement I need to understand why \left|4+i \right|=4.123 and why this is shown by: \sqrt{4^{2}+1^{2}}=4.123 Homework Equations i^{2}=-1 The Attempt at a Solution If I find the square root of this expression squared, then I come up with \sqrt{16-1+8i} which is...

Homework Statement I don't know how to find the square root of a complex number in rectangular form? As in, say, \sqrt{}9-6i..my calculator can't do such an operation (yet my graphics calculator can, which can't be used in exams), so how do i go about to do this 'by hand'? I just found...

Homework Statement I'm working on a circuits equation and need to find V(o). The equation is: (V(o)/-j25)+((V(o)-240)/12.5)+(V(o)/(15+j20))=0 How do I solve for V(o)? I know the answer is 183.53-j14.12, but I don't understand how to get to that answer. Thanks in advance! Homework...

Homework Statement Find all complex solutions to: conjugateof(z) = 2*z + (1 - i) Homework Equations The Attempt at a Solution conjugateof(z) = 2*z + (1 - i) I make: z = (a + bi) and conjugateof(z) = (a - bi) which gives: (a - bi) = 2*(a + bi) + (1 - i) then to find...

Homework Statement I have this equation and need to find |F|2 (which should be real). I thought you did this by multiplying by the complex conjugate which was just replacing all i with -i, but this doesn't seem to work. What am I doing wrong? Thanks Homework Equations The...

I have a problem in understanding the procedures of a solved example. It goes like this. \left ( \frac{z+i}{z-i} \right )^4 = -1 Therefor we can write: \left | \frac{z+i}{z-i} \right | = 1 From that we can see that z is a real number because: \left | z+i \right | = \left | z-i...

Homework Equations I was just wondering, how do you guys get the argument value from a complex number without using any calculator, i know that some solutions may be impossible to get without a calculator but just finding some of the easier angles. The Attempt at a Solution...

Homework Statement if z = -2 + 2i find r and θ The Attempt at a Solution our teacher told us that when we have z = a + bi r = sqrt(a^2 + b^2) and θ = tan^-1(b/a) so here it's supposed to be r = sqrt(8) and θ = - pi/4 but using wolfram alpha to see if the results are...

z_k=\sqrt[n]{u}=\sqrt[n]{r}e^{i\left(\frac{\phi+2k\pi}{n}\right)}, k=0,1,2,...,n-1 and z_k=\sqrt[n]{u}=\sqrt[n]{re}^\frac{\phi+2k\pi}{n}, k=0,1,2,...,n-1 Which one is incorrect (note that in the first, e is out of the root)?

Complex Number Question - Euler's Formula? Homework Statement Express (-2 + 2i)^10 in the form re^(iθ)Homework Equations Euler's Formula, I think? The Answer given is: (2√2)^10 e^[i(15pi/2)] The Attempt at a SolutionI don't know what I'm doing wrong here; r = √[(-2)^2 + 2^2] = √8 =...

Homework Statement Let z1 = 4 + 3i and z2 = 2 - 5i. Find each of the following in the form x + iy, showing the details of your work: I'll show in the photo the 2 questions i require help with. Homework Equations Complex numbers The Attempt at a Solution attempted f) 1/z^2 =...

Hi, I need to do Interpolation of complex numbers let say z1=x1+i*y1 and z2=x2+i*y2 now I have two approaches: 1) interpolate real and imaginary parts separately and have the result or 2) First change the complex numbers into (R,Theta) co-ordinate and then do the interpolation on R and Theta...

Hello, I need to simplify and find Re and I am of . I've multiplied by and got that Re= and Im=. Is that the correct way and a correct result ?

Homework Statement z=\frac{(1-3i)^{100} * i * (7-5i)}{5+7i} Homework EquationsFind module and argument of z. The Attempt at a Solution Assuming: |z_1 * z_2| = |z_1||z_2| |z|=\frac{|1-3i|^{100} * |i| * |7-5i|}{|5+7i|} And now calculate each module individually by "Pythagoras theorems"...