Complex numbers Definition and 730 Threads

Hello I got some funny idears don't know if they are true, but I will share them with you. Homework Statement I would like to prove these formula (1)sin(z_1 + z_2) = sin(z_1) \cdot cos(z_2) + sin(z_2) \cdot cos(z_1) (2)cos(z_1 + z_2) = sin(z_1) \cdot sin(z_2) - cos(z_2) \cdot...

Homework Statement Express -i in polar form, using the principal value of the argument. Homework Equations modulus = \sqrt{a^2 + b^2} \theta = arg(0 - i) The Attempt at a Solution Well, the complex number is 0 -i. a = 0, b = -1 so: r = \sqrt{0^2 + (-1)^2} which comes out to...

Hello guys; I'm after a bit of help here, I may have missed something completely obvious, but I can't seem to figure out the working of: 1 + i = √2(cos π/4+ i sin π/4) ie; How does 1 + i equal √2(cos π/4+ i sin π/4)?? any help would be appreciated; Thanks Craig :)

1. Complex analysis is the study of number z= x+iy where i^2=-1. can you find a way to represent complex numbers as 2x2 matrices i honestly have no clue where to start with this one. we are one week through my linear algebra course. the only possible thing i can thing of is det (x -yi...

Here is another problem that I'm not sure how to approach A Circuit consisting of a 500 Ohm Resistor in series with a 1.2 micro F capacitor is connected to a supply at a frequency of 400Hz. Use complex numbers to determine the values of resistance R and capacitance C, that when connected in...

Hi, here is the problem.. The potential difference across a circuit is represented by 40 + j25 volts, and the circuit consists of a coil with an inductance of 0.06H in series with a resistance of 20 Ohms. If the frequency is 80Hz find the complex number in rectangular form that represents the...

I'm currently studying complex numbers in my high maths class, moving onto trigonometry. I already know some applications of complex numbers, such as phase differences in capacitive and inductive circuits, but what other applications are there? Can they be applied to circular motion in...

I was wondering if someone can check my solutions and perhaps give me a faster more logical way of working through this question. Thanks. Homework Statement If z = 1 + i*root3 i) Find the modulus and argument of z ii) Express z^5 in Cartesian form a + ib where a and b are real iii)...

Homework Statement Describe the locus of points z satisfying the given equation. Homework Equations Im(2iz)=7 |z-i|=Re(z) The Attempt at a Solution I started on the second one: I think that Re(z) is just x, then I squared both sides, simplified and got (y-1)^2=0 is this...

Problem: (I don't have latex/mathtype for this sorry in advance) Let n,k both be in the Natural Numbers n does not divide k (I have already completed the case when it does) Show that the series: 1 + e^i(2pik/n) + e^i(4pik/n) + ... + e^i[(2n-2)pik/n) = 0 Using eulers formula e^ix =...

Firstly I do apologise, because this question is got more to do with the mathematical side of Electronic Engineering, because my mathematical classification is not that good I don't know where I would put this question on the mathematics section, if any of the moderators or whoever can, wants to...

Hello everyone.. I have quite a problem regarding A.C. circuit analysis using complex numbers and 2x2 matricies. * The aim is to find the current in each of the two loops and apply Kirchoff's laws. I believe the overall aim is just to prove that the laws are actually in place.. (SEE...

Hi! I've got a question. There is a nice formula for finding square roots of arbitrary complex numbers z=a+bi: \frac{1}{\sqrt{2}}(\epsilon\sqrt{|z|+a}+i\sqrt{|z|-a}) where epsilon:=sing(b) if b≠0 or epsilon:=1 if b=0. I've just looked it up and it's nice to use it to find complex roots of...

Hello all I am having this problem with complex number and i don't know exactly how to solve it. Can i get some help with it please: i) Z1 = 2 + j5, Z2 = 1 – j3 and Z3 = 4 – j determine, in both rectangular and polar form, value of ((Z1 * Z2)/(Z1 + Z2)) + Z3 (Give the final answers to...

1/z is 1/(x+iy) however, i then multiply by the complex conjugate and get: (x-iy)/(x^2+y^2) now, how do i graph this? thanks.

Re^{j \theta} = R{(cos \theta + jsin\theta )} can anyone show me this proof or show me a link please

This is a question that's stumping both myself, and my friends who are on maths degrees! So... cos(x) can be written as \frac{1}{2}(e^{ix}+e^{-ix}) correct? so does that make its conjugate \frac{1}{2}(e^{-ix}+e^{ix}), i.e. cos(x) again? or does the switching of the sign go in front of the e...

it says to use exponentials to prove: tanh (iu) = i tan u however i do not get the correct relationship, is this an error in the question perhaps

[Deleted]. Figured it out

How can i write for example: 2cis(pi/3) in my ti83+ calculator? how do i write cis?

complex numbers problem -HELP! i have thinking about this problem for atleast 2 hours but still it hasnt struck me : Show that the locus of z, which satisfy arg(z-1/z-2)=pi/4 is the major arc of a circle.Also find centre and radius of corresponding circle. (this problem is from FIITJEE (an...

Hey if anyone could help me to understand wat to do in this question I would be appreciative! Find in the complex plane the fourth roots of -64, Use the result to factor Z^4+ 64 into i) a product of four linear factors I kinda thought that you could write something along the lines of this...

What is the relationship between complex numbers and vectors in a plane? I read they have the same mathematical structure. What does that mean and how far does that sameness go? If the complex numbers are all ordered pair that obey (a,b)+(c,d)=(a+c,b+d) and (a,b)(c,d)=(ac-bd,ad-bc), can we...

"Use Demoivre's Theorem to find the indicated power of the complex number. Write the result in standard form." : 2(squareroot of (3) + i)^5 now when i do this i always end up getting -(32squareroot(3))/2 + i32/2 the book seems to get teh same answer except WITHOUT the 2 in the...

I am programming a module used to convert measurement units. This will be part of a system that supports complex numbers. I never use complex numbers in my field but of course engineers and physicists do so I thought I should ask a couple of questions first. Q1. Is there anything unusual about...

need a lil help here thnx

I have the two series: C = 1 + (1/3)cosx + (1/9)cos2x + (1/27)cos3x ... (1/3^n)cosnx S = (1/3) sinx + (1/9)sin2x ... (1/3^n)sinnx I have to express, in terms of x, the sum to infinity of these two series. Here's what I've done so far: Let z represent cosx + jsinx C + jS = z^0 +...

find the four roots of the equation z^4 + 7 -24i = 0 completely lost, some help please...

Hi, I have no clue how to approach this question, was in my last years final exams. (z^2 + 1)^4 = 1 Find all solutions, where z is a complex number. Tips please?

Hi, can someone please help me with the following question? Q. Let \omega _0 ,...,\omega _{n - 1} be the nth roots of 1. Show that \sum\limits_{j = 0}^{n - 1} {\omega _j ^k } = \left\{ {\begin{array}{*{20}c} {0,1 \le k \le n - 1} \\ {n,k = n} \\ \end{array}} \right. The...

Hey, I'm finding equivalent impedances of circuits, and I always run into things like this: 1/(-j25) + 1/(600 +j900) = 1/Zeq I don't know how to proceed from here. I know this is more of a math issue than anything else, but I appreciate your help

Complex numbers tutorials please Hi i need some good online tutorials about complex numbers.. I need to start from scratch and to move to more advanced topics. Do u have anything in mind? Thx a a lot

Complex numbers ... help needed! In our exercises we are told to solve for x (element of a complex number) 1. x^2 - 6x + 25=0 The answer is x=3+4i or x=3-4i Can anyone tell me how these answers were derived??

Hi i need some good articles about complex number and more especially with complex envelopes...Do u have anything in mind? Thx a lot

I have z=-(1/2)-(sqrt3/2)i r=|z| is this right? r=cos*2Pi/3+i*sin*Pi/3 = 1 + sqrt3/2*i Now I have to find Z^2004, how do I do that?

I recently was confronted by this monstrosity of a question in one of my mock exams. |Z1 + Z2| ≤ |Z1| + |Z2| I made a few attempts at it before becoming demoralized with the lack of progress.. |Z^2| was equal to Z1(conjugate)Z1 Hence equaling X^2 + Y^2 However even when expanding...

Please help with these simple questions just not understanding it properly. Find square root, of -6i let sqroot of -6i= x+ yi then -6i=x^2 - y^2 +2xyi x^2 - y^2 = 0 and 2xy=-6 then xy=-3 x=-3/y and then solve simu.. i got y= 3 and x=-1 y=-3 x=1 so the anser is +_(-1+3i) BUt that...

Complex Numbers---Plz Help Hi Guys! well can anyone recommend me websites where i can get some knowledge and techniques to deal with complex numbers especially those which use De Moivres Theorem and Euler's Forumale. Thanks in advance

Anyone got a good link to a place that explains complex numbers?

Hi, I desperately need help with this qns: In an Argan Diagram, the points A, B, C, D represent the copmlex numbers a,b,c,d respectively. Guiven that ABCD is a rectangle describd in an anticlocwise sense, with AB=2CB, and a=-2-i, c=3+5i, find b and d (AB and CD are not parallel to the xaxis)...

Hi, I desperately need help with this qns: In an Argan Diagram, the points A, B, C, D represent the copmlex numbers a,b,c,d respectively. Guiven that ABCD is a rectangle describd in an anticlocwise sense, with AB=2CB, and a=-2-i, c=3+5i, find b and d Any help is greatly appreciated, thnx...

There are n nth roots to every complex number (except zero). My question: How many "roots" are there when you take a complex number to an irrational or transcendental number. For that matter, how do we define raising a number to an irrational number? How do we define raising a number to a...

Hi, I've been working on some ODEs and I've been using all of the standard techniques. Recently, I came across some solutions to some IVP problems(I don't have the questions, only the solutions). I'm curious as to the motivation behind the follow technique. As in, why would this method be used...

Hi I'm struggling with the following questions where I need to sketch Argand diagrams. I haven't had much exposure to a wide range of these sortsof questions before so I'm not finding the following to be all that easy. There are a couple and some help would be good, thanks. 1. |z| < Argz...

How can I calculate cos 72° and sin 72° using complex numbers, and without the use of a calculator? I noticed that 5*72° = 360° so (cos 72° + i*sin 72°)^5 = 1. But, I don't quite know how to go from there.. :shy:

Suppose z1 = a + bi, z2 = c + di are complex numbers. When does |z1 + z2| = |z1| - |z2|? (with || is modulus) It seems obvious that this is the case when z2 = 0, but are there other solutions? According to the book, no. But after 2 days, I still cannot solve it! :cry: Here is what I...

OK, I've got this question to do: Find complex numbers representing the vertices of a triangle ABC given that the midpoints of the sides BC, CA, AB are represented by complex numbers z_1, z_2, z_3 respectively. Thing is, I don't know where I'm taking the origin to be; if I took it at A...

If you have a 2-D vector in polar coordinates (a magnitude R and an angle theta) you can convert it to Cartesian coordinates with the following equation: x + yi = R e^{\theta i} Or from Cartesian to polar by: (R,\theta) =ln (x + yi) Why does this work? I just can't quite envision...

The advanced topics in complex nos are really boring and make no sense. Is there any way I can make them interesting like any software or book which would make it easier and enjoyable?

Just wondering if anyone could help me out with some problems I'm having with differential calculus. Firstly, can anyone confirm if I sketched the region in image 1.jpg correctly (shown in 2.jpg)? I've done questions before where it just says |z|<2 and I know that it looks like a circle, but...