Complex numbers Definition and 724 Threads

Let <zn> be a sequence complex numbers for which Im(zn) is bounded below. Prove <e^(i*zn)> has a convergent subsequence. My question on this is what possible help could the boundedness of the Im(zn) to this proof and what theorem might be of help?

Homework Statement I'm asked to describe geometrically the set of points in the complex plane describing some equations. I got them all right except this one: |z+1| + |z-1| = 8 Homework Equations |z| = sqrt( x2 + y2 ) The Attempt at a Solution Well, I know that an equation of...

Hey everyone! Here I have a problem I don't know how to solve so help would be greatly appreciated! Homework Statement Here is an equation z^3+az^2+bz+c where a, b and c are real numbers. If the roots are drawn in the complex plane they form a triangle with area of 9 units. One root of the...

The initial development of QM inherited the use of complex numbers from Fourier analysis. Had Hartley analysis been invented first, is it possible that QM might have been formulated in terms of real-valued quantities instead, or are complex numbers in some sense natural or necessary when...

Homework Statement Find the current in them in this circuit, if we know R=X_L, X_C and u=5sin(314t) The Attempt at a Solution First , 5=U_0, 314=\omega and voltage we can write as u=U_0cos(\omega t + \frac{\pi}{2}) and u=U_0 e^{i\frac{\pi}{2}}=iU_0. U is the voltage at the source U_1 in...

Yes, they make things simpler. But how? I've never come across a comparison of life with complex numbers and without? Can some one point me to an example or give one. An electrical engineering example would be great.

Hello everyone, I need some help with the following: I understand that by using xn = axn-1+b we can generate a full sequence of numbers. For example, if x1=ax0+b, then x2 = ax1+b = a2x0+ab+b, and so on and so forth to xn. I need help applying this same concept to complex numbers (a+bi). Is...

Homework Statement Show that if z_1,z_2 \in \mathbb{C} then |z_1+z_2| \leq |z_1| + |z_2| Homework Equations Above. The Attempt at a Solution I tried by explicit calculation, with obvious notation for a,b and c: my frist claim is not that the triangle inequality holds, just that...

[b]1. I have been asked to add 1/z1+1/z2+1/z3=Y. When z1=2+j2 and z2=1+j5 and z3=j6. [b]3. I have basically treated them like a normal resistors in parallel equation using 1+j0 and dividing them individually and then adding the product to get Y=0.29-j0.55. Is this the right way to go about...

Hi, I have a complex number and understand that the rectangular form of the number is represented by s = σ + jω, where σ is the real part and jω is imaginary. I am having trouble locating them in the number below: I know that "2" is a real number, and the numerator is imaginary...

Hello. I maybe should have put this in the maths section, but it is related to electronics, so I figured here. I am reading Microwave Engineering by Pozar, and in one of the examples, it says that the series RC load impedance is ZL = 60 - j80, so the resistance is 60 Ohms and the...

Homework Statement Show that if p is prime and e^{2 \pi i/p} is constructable then p=2^k+1 for a positive integer kHomework Equations e^{i \theta} = Cos \theta + iSin \theta The Attempt at a Solution By definition, a complex number a+bi is constructible if a and b are constructible...

Homework Statement Write the equation of a circle in complex number notation: The circle through 1, i, and 0. Homework Equations The Attempt at a Solution I know the equation for a circle with complex numbers is of the form |z-a| = r where a is the center point and r is the...

Are there any numbers that is not considered to be a subset of a complex number subset of a + bi Where a and b are real numbers?

any help with me understanding this problem would be very much appreciated. Homework Statement show, ^{π/2}_{0}\int cos^{5}xdx = 8/15 hence show ^{π/2}_{0}\int sin^{5}xdx = ^{π/2}_{0}\int cos^{5}xdx where, cos^{5}θ = \frac{cos5θ + 5cos3θ + 10cosθ}{16} sin^{5}θ = \frac{sin5θ -...

How do you go about sketching y as a function of t for t≥0 y= e(0.5t + i(√7/2)t) - e(0.5t-i(√7/2)t) I know it goes through the origin, and the gradient is positive here. But I'm unsure on how to deal with the imaginary numbers when I have a graph of y vs t.

Fourier series of complex numbers with diffrent limits of integration? Dear all, i don't know how to simplify a COMPLEX NUMBER Fourier series with LIMITS OF INTEGRATION that are not complementary. I MEAN limits LIKE this X to -X being easy to solve and SIMPLIFY but Not X to -Y or...

Need help with this please: Homework Statement (1 + cosθ + isinθ) / (1 - cosθ - isinθ) = icotθ/2 The first step in the solutions shows: (2cos^2θ/2 + i2sinθ/2cosθ/2) / (2sin^2θ/2 - i2sinθ/2cosθ/2) Homework Equations I can't get there. The Attempt at a Solution I tried multiplying by: (1 -...

Homework Statement I am doing a problem where I have to design a controller for a system. I have to solve the below equation for ω 3.1 (ω)^2 - 6.2iω - 20 Homework Equations The Attempt at a Solution I am not sure how to start It looks like a quadratic but I don't know what to...

Friedberg's Linear Algebra states in one of the exercises that an inner product space must be over the field of real or complex numbers. After looking at the definition for while, I am still having trouble seeing why this must be so. The definition of a inner product space is given as follows...

Homework Statement For H \leq G as specified, determine the left cosets of H in G. (ii) G = \mathbb{C}* H = \mathbb{R}* (iii) G = \mathbb{C}* H = \mathbb{R}_{+}The Attempt at a Solution I have the answers, it's just a little inconsistency I don't understand. For (ii) left cosets are...

For matrices, Schur product or Hadamard product is defined as the entry wise product. I want to know if they have a similar type of multiplication for complex numbers. That is (a+ i b) o (c + i d) = (a c + i b d) I encounter a situation where such a definition is useful. In physics I get...

Homework Statement given that kλ2-ρcpuλ-ρcpωi=0 plug into the quadratic formula and get out an equation that looks like this λ=α+iβ±γ√(1+iδ) where α,β,γ,and δ are in terms of ρ,cp,u,k, and ω Homework Equations (-b±√b2-4ac)/2a kλ2-ρcpuλ-ρcpωi=0 λ=α+iβ±γ√(1+iδ) The Attempt at a...

Homework Statement What are the phasors F(t) and G(t) corresponding to the following functions: f(t) = Acosω1t and g(t) = Acosω2t Draw the phasors on Argand diagram as well as F(t)+G(t) at t = \pi/(2ω1) and from the diagram get f(t)+g(t) as a cosine identity in the simplest form...

Homework Statement Please help me find (3/(1-i)-(1-i)/2)^40. I got a result (see below) but I'm not sure whether it is correct. Any help is appreciated. Thanks. Homework Equations The Attempt at a Solution I got (1+2i)^40. After this I got some funny numbers like...

Homework Statement [b]1. I'm trying to figure out how to take limits involving i and complex functions f(z) The first problem is as follows: lim(n \rightarrow \infty ) n*((1+i)/2))^n The second is: lim (z app. 0 ) of (sinz/z)(1/z^2) The third is: lim (z app. e^i*pi/3) of...

Homework Statement show that: I tried changing the form to the sin and cos, but I couldn't complete it.. Any hints?

Consider an Argand diagram that shows the number line (positive and negative) and the imaginary plane of other possibilities. As in, we have numbers that are positive and negative, and through complex numbers all of the polarities in between. I am using this as an analogy, because we have...

Following are problems from the book "Complex Numbers from A to ...Z" by Titu Andreescu and Dorin Andrica. It's a wonderful book, I'm still adapting to the higher-than-usual level though. My questions/comments are written in bold throughout the problems and solutions. Problem 1: Prove that for...

Patterns from complex numbers ! URGENT! - Use de moivre's theorem to obtain solutions for z^n=i for n=3, 4 and 5. - Generalize and prove your results for z^n=a+bi, where |a+bi|=1. - What happens when |a+bi|≠1 Relevant Equations: z^n = r^n cis (n\theta) r = \sqrt{a^2 + b^2}...

Homework Statement I'm in differential equations right now and we are about to start Laplace Transforms. Our homework is over complex numbers: Simplify the following equation: 1+cos(\theta)+cos(2\theta)+cos(3\theta)+...+cos(n\theta) Homework Equations The Attempt at a...

If the Gamma function \Gamma (z) = \int_0^{\infty} t^{z-1} e^{-t}\;dt only converges for \text{Re}(z)>0 then why is, for example, \Gamma (-1+i) defined when clearly \text{Re} (-1+i)<0 ?

Homework Statement Find four complex numbers z each with the property that Re(z), Im(z), Re(z-1), Im(z-1) are all integers, where Re and I am denote the real and imaginary parts respectively of a complex number. Homework Equations Maybe 1/z = \frac{\bar{z}}{|z|2} ? On my screen that code...

Hey, I'm not too sure if this is pre-calc or not because it's in a different course but I think I remember doing this in pre-calc a long time ago... 1. Determine cartesian(z = x + jy) and exponential(\rhoe^{j\theta}) forms of the following complex numbers: z = 3 + 5j 2. I have no...

Homework Statement Let a, b in R, not both zero. Find c, d in R such that (a+bi)^-1 = c+di Homework Equations i^2=-1 R is the set of all real numbers The Attempt at a Solution I have a feeling I'm approaching this problem incorrectly but: 1 = (a + bi)(c + di) =ac + adi + cbi + bdi^2 but...

"Solving Inequality With Complex Numbers" Question Homework Statement What does the inequality pz + conjugate(pz) + c < 0 represent if |p|^2 >c ? Homework Equations p is a constant and a member of the set of complex numbers. c is a constant and a member of the set of real numbers...

Homework Statement Determine the region in the complex plane described by |z-2i| < |z+ i| Homework Equations z= x+ iy |z|= (x2 + y2)1/2 The Attempt at a Solution |z-2i| < |z+ i| |z-2i|/|z+ i| < 1 |z-2i| = [(x-2i)2 + y2]1/2 |z+ i| = [(x+i)2 + y2]1/2 [(x-2i)2 + y2]1/2...

Does it have something to do with the quadratic form? What would i type on google to search for more information to get better search results?

Complex analysis gives us theories about functions that u can't get without the complex algebra, could there be an extension to complex numbers that might solve important problems in mathematics.. Thanks to all..

Homework Statement What is the square root of z=-9Homework Equations The Attempt at a Solution Is it possible of me to not use De'Moivre's theorem to solve this question?? Solution : z= \sqrt{-9} z=\sqrt{9} x \sqrt{}-1 z=\pm3 i Will this method be acceptable?? Is this still under the topic...

this wikipedia article http://en.wikipedia.org/wiki/Qubit says i am kind of comfortable with the physics of it, but i am totally lost on the thing about vector space over the complex numbers can someone please lend me a hand? it seems that the more i try to read about it, the less i know

Hey People just a general question Is the following necessarily possible? |z23|=|z|23 Where z is a complex number. I can't think of a reason why not but then again complex numbers have some subtle behaviours. Thanks

Homework Statement Let V = C (complex numbers). Prove that the only C-subspaces of V are V itself and {0}. Homework Equations The Attempt at a Solution Well this problem has me confused since I have clearly found a complex subspace for example all the complex numbers of the form {a+ib ...

Hi, I recently bought an HP50G, and I'm having trouble figuring out how to get numbers from the stack into a complex number. Could anyone help? For example, for 1+2i, I know I'd enter it as (1,2). But when I have something like 6^0.5+2i, I don't want to type the numbers out. Thanks Edit...

Homework Statement http://www-thphys.physics.ox.ac.uk/people/JamesBinney/complex.pdf Example 1.2 (Page 6) Homework Equations De Moivre's Theorem, Euler's Formula, and other simple complex number theory formulas The Attempt at a Solution I'm having troubles understanding the format, which...

Homework Statement Let z1; z2; z3; z4 be four complex numbers on the unit circle (i.e., |z1|=|z2|=|z3|=|z4|=1). It is known that z1+z2+z3+z4=1+i . Find the value of 1/z1 + 1/z2 + 1/z3 + 1/z4 Homework Equations 1/z = barZ/|z|^2 The Attempt at a Solution I've been trying for about a day now...

I have to find x and y for: (x+y)+i(x-y)=14.8+6.2i how to do?

Solve the following simultaneous equations for the complex variables i1 and i2. 2= (3-j)i1 - (5-j2)i2………………(1) 12 = (2+j)i1 + (1+j6)i2………………(2) Not sure how to attempt this question please can you help. Thanking you in advance Jake

I'm working my way through Shaum's Outline on linear algebra and in it they define a complex number as an ordered pair of real numbers (a,b). So given a real number a, its complex counterpart would be (a,0). Operations of addition and multiplication of real numbers work under the...

I have read from my algebra book that the product of two complex numbers is still a complex number: (a+bi)(c+di)= (ac-db)+(bc +ad)i I was thinking that since complex numbers can be used to represent vectors, the product of two vectors should still be a vector. But I have also read from my...