Polar form Definition and 101 Threads

Hello All, I'm reviewing some notes for a course and am confused by one step that they do. They are deriving an equation for the ampiltude of a wave that is being damped and driven by a force. I understand it all except for one step in which they state that: (\omega_{o}^{2} - \omega^{2}) -...

I got this equation 5<0° = -14.14<-45° + 2.24<116.6° I2 And i solved I2 this way I2 = -14.14<-45° / 2.24<116.6° I2 = 8<150.29° I want to know complex numbers is the same way as normal math or not thanks in advance

Homework Statement Convert the following Cartesian equation to polar form. x^2/9 + y^2/4 = 1 Homework Equations r*cos(t)=x r*sin(t)=y r=Sqrt(x^2 + y^2) y/x = Arctan(t) The Attempt at a Solution I get ugly looking things like r^2(cos^2(t)/9 + sin^2(t)/4) = 1 but being a simple ellipse (edit...

Homework Statement Convert -2^i to polar and rectangular form Homework Equations mag(a+ib)=sqrt(a^2+b^2) exp(i*angle)=cos(angle)+i*sin(angle) The Attempt at a Solution im not sure how to get the polar (or rectangular form) of -2^i. i know the answer is exp(-2.448rad)... i just don't know the...

Homework Statement Show that the solution x(t) = Ge^(iwt), where G is in general complex, can be written in the form x(t) = Dcos(wt - \delta). D(w) and \delta(w) are real functions of w. Homework Equations z = Ae^(i\phi) The Attempt at a Solution So I know I should start by...

Homework Statement H(F) = 5/(1+j2piF/10) Rewrite in polar form, that is, in terms of magnitude and phase. Homework Equations The Attempt at a Solution phase is the 2piF/10 but I'm not sure how I account for it being on the bottom of the fraction

I know that a complex number can be written in form of a+bi and r(cos(theta) + isin(theta)) but I don't understand the the representation of it as r*e^(i * theta) also

Express the following in cartesian curves in polar form i) 4x-5y=2 Not sure how to do this ii) (x-3)^2+(y-4)^2=25 r=9cos16(theta) Is this correct ? Any help would be great

Homework Statement The planets travel in an elliptical orbit with the sun as a focus. Assume that the focus is at the pole, the major axis lies on the polar axis and the length of the major axis is 2a. Show that the polar equation of orbit is given by r=\frac{(1-e^2)a}{1-e\cos\theta} here's...

Homework Statement (5∠2.214)/(√5∠-1.107) ive gotten this far in a problem(thats the answer but i need to simplify).. all i need to know is how to divide the angles? Homework Equations The Attempt at a Solution

I really, really need to know the formula that adds (or subtracts) two complex numbers in polar form, and NOT in rectangular form. I know there is such formula (I saw it in some book), and it's composed of cosines and sines. Please, please don't tell me to convert back to rectangular form...

Homework Statement Find the polar form of 2i − 1 Finding polar form is easy r(cosx + isinx) call the real part a and imaginary part b r = sqrt(a+b) theta = arctan (-2) = - 63.43 This is the wrong angle for theta as it's 116.57 (which is 180 - 64.43), and I guess this if...

Homework Statement evaluate i^1/4 Homework Equations - The Attempt at a Solution don't know how to find the angle on argd

Homework Statement Convert t = pi/6 into polar form. Homework Equations x = r*cos(t) y = r*sin(t) The Attempt at a Solution t = pi/6 cos(t) = cos(pi/6) cos(t) = sqrt(3)/2 x/r = sqrt(3)/2 sqrt(3)r = 2x sqrt(3)sqrt(x^2 + y^2) = 2x sqrt(3x^2 + 3y^2) = 2x 3x^2 + 3y^2 = 4x^2...

Homework Statement What is the polar form of the complex number 3-4i? Homework Equations z=r*cos(theta)+i*r*sin(theta) The Attempt at a Solution 5(cos(arctan(-4/3))-i*sin(arctan(-4/3))) This is what I thought the correct answer would be, but it was a multiple choice quiz and...

Homework Statement a) r=a(2+ cos(\theta)) Find the area of the region enclosed by the curve giving answers in terms of \pi and a b) Show that the area enclosed by the loop r=2(1-sin(\theta))\sqrt{cos(\theta)} is \frac{16}{3} and show that the initial line divides the area...

Homework Statement (1+i)i = reiθ Find the real values of r and θ. The Attempt at a Solution Well, after doing a similar(ish) question I decided taking logs would be a good start: i loge(1+i) = loger + iθ From here, I have no idea where to go. Using a power of i is killing me...

Homework Statement a) Find the area enclosed by the curve r=2+3cos(\theta). b) Find the area enclosed by the curve (x^2+y^2)^3=y^4 (after converting to polar form) Homework Equations The general equation for the area of a sector of curve: A=\frac{1}{2} \int_{\beta}^{\alpha} r^2...

Homework Statement I have a motor with a full load output rating of 2.8 kW with an effciency off 70% and at 80% of full load runs with a Power Factor of 0.8 lagging. A second motor has afull load output of 4.2kW with an effciency of 85% and at 80% of full load runs with a PF of 0.75...

Homework Statement I am having difficulty with a question on my Electrical course and the expressing a motor load voltage and current in polar form. The motor is single phase 2.8 KW efficiency 70% and 80% of full load runs with a power factor of 0.8 lagging. Voltage 400v. Express the motor...

Homework Statement Hi guys I have been given a question, write down w* in polar form where w=2< -(pi/3). I can work out the question when it is in cartesian form just not this way, any help woud be great. Homework Equations The Attempt at a Solution

I'm sure my question is very simple to most of u guys. But I have the following confusion. Let's say we have an AC voltage source in a circuit. In rectangular form it's phasor form is v= -4 - 16 j . I want to write this phasor in polar form. Well, The phasor is in 3rd quadrant of complex...

-1-(under root)3 i here we find that r=2(hypotenuse) a=-1(base) b=-(under root)3 when i take sin theat= p/h=-(under root)3 / 2 theat from sin is -60 when i take cos theta = b/h =-1 / 2 which gives 120 now one is -60 and other is 120, which is the angel , i have to follow and what...

Homework Statement Compute the 4th roots of -16 in both Cartesian and polar form and plot their positions in the complex plane. Homework Equations z^1/n=(r^1/n)(e^i(theta)/n), (r^1/n)(e^i(theta)/n)(e^i2(pi)/n... The Attempt at a Solution How do I find the value of r, and theta??

Homework Statement Evaluate the square 0f 5e^(3(pi)i)/4 without using Cartesian form, and also the three different products. Homework Equations e^i(theta) = cos(theta) + isin(theta)? The Attempt at a Solution I have absolutely no idea here, nothing in my notes even begins to...

Hi, I have two voltages given as v1(t) = 20cos(\omegat - 45) and v2(t) = 10sin(\omegat + 60) My task is to add them on the single form Vcos(\omegat + \theta) The first part is relativley easy: The phasors are v1 = 20\angle-45) and v2 = 10\angle-30) so i have 20\angle-45) +...

Hi I need to use a double integral to find the area of the region bounded by: r = 3 + 3sinQ where Q = theta. I know the bounds of the inner integral are from 0 to 3 + 3sinQ. However, I do not know how to determine the bounds of the outer integral. Any help would be greatly appreciated.

Hi I need to use a double integral to find the area of the region bounded by: r = 3 + 3sinQ where Q = theta. I know the bounds of the inner integral are from 0 to 3 + 3sinQ. However, I do not know how to determine the bounds of the outer integral. Any help would be greatly appreciated.

Homework Statement I am looking for the fifth roots of unity, which I believe come in the form of: cos(2kpi/5) + isin(2kpi/5), k=1,2,3,4,5 and when k=5, the complex number is 1. how do you convert the rest to complex numbers? Normally, I use common triangles like: 45-45-90 and...

There are plenty of interesting plots that use various ways to plot the integer occurrences of a^2 + b^2 = c^2 such as making ordered pairs (a,b) and doing that for all such that a^2 + b^2 < [a really big number] and very interesting patterns are noted. My thought is plotting a polar analog...

What is the difference between Complex Numbers in polar form as opposed to rectangular form?

hi! i need some help here, do you have any available example on how to find the arc length in polar form θ = f (r)? using integral calculus, i mean. i searched the internet but i only got the r= f(θ) example. i hope you can help me. thanks!:)

Hi There. I was given this question and the answer: Find the polar forms of 1/z where z = \sqrt{}3 + i and 1/z where z = 4\sqrt{}3 -4i Answers respectively are: 1/2 cis(-\pi/6) 1/8 cis(\pi/6) Can someone please explain to me why it is that the sign of the argument...

Hi There, Can someone please tell me where I can find a table/ data that converts radians to surds. I don't know what to call it but, for instance to tan^-1(-1) = -Pi/4 and, cos(-pi/6) = root3/2 ? Thank you :)

Hi I found this problem in the Fundamentals of Signals and Systems by Boulet problem 1.1 find the polar form of following signal. x(t) = t / ( 1 + it) I know Amplitude = |t| / (\sqrt{(1 + t^{2})} now how do we find the phase. Any help is appreciated.

[SOLVED] Latitude Longitude -&gt; Polar Form -&gt; Cartesian Coordinates Homework Statement I need to convert 46 Degrees North 80 Degrees west into Cartesian coordinates, based on the assumption that the Earth is a sphere (althought it's not). Homework Equations...

Homework Statement Problem from Arnold's "Mathematical Methods of Classical Mechanics" on page 59. Find the differential equation for the family of all straight lines in the plane in polar coordinates. Homework Equations \Phi=\displaystyle\int^{t_2}_{t_1}...

Homework Statement I solved this following problem but I am not sure whether I did this right: convert (1/(2^j)) to cartesian form. Homework Equations The Attempt at a Solution re^j\theta = a+jb a=r cos \theta= cos -\pi/2 b= sin -\pi/2 = -1 1/(2^j) = 2^-j...

Homework Statement Convert cos(7 t) + sin(7 t) into polar form of A cos(\omega_0 t - \delta) This is a review problem where once we convert this to polar form we are to give amplitude, period and delay (shift). I can answer this question if someone can point me to a website tutorial...

hello i have this problem about polar form, i am aware that when you have a problem like \int\int x^2 + y^2 dxdy you use r^2 = x^2 + y^2 but i what would you do if you had a problem like \int\int xy dxdy? thanks in advance. edit: i know the limits if you need them please let me know but i...

Complex numbers - polar form - does this work (indices) ? hey i haven't studied in class complex numbers yet, but i know some of the basis , and i was wondering if something i saw in complex numbers was true : polar form : let 'a' be the angle and x the length (dont know how to call it...

Homework Statement I need to get y = mx in polar form. I looked at it logically, and I figured I needed a function f(x) that will resolve 0 when x =/= 0, and will resolve 1 when x = 0. I thought for a while, and then realized that sine sort of does that, and just needs a tweak to do it exactly...

Homework Statement Write equation in polar form. y=3x+4 Homework Equations x^2 + y^2 = r^2 x = rcos(theta) y = rsin(theta) tan(theta) = y/x The Attempt at a Solution Square both sides... y^2 = 9x^2 + 24x + 16 r^2 - x^2 = 9x^2 +24x +16 r^2 = 10x^2 + 24x + 16 And...

IS there a formula for: z=(Cosx +iSinx)^4 (Cosy + iSiny)^2 ??

Homework Statement The question: a)Solve the equation z^{3}=4\sqrt{2}-4\sqrt{2}i.. b)Express the answer in polar form. The Attempt at a Solution Here's what i got: r=\sqrt{\left(4\sqrt{2}\right)^{2}+\left(-4\sqrt{2}\right)^{2}}=8 \tan^{-1}\left(\frac{-4\sqrt{2}}{4\sqrt{2}}\right)=-45^{o}...

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

i have the integral \int_{0}^{\infty} \int_{0}^{\infty} (-x^2-y^2) \ dx dy (double integral with both limits the same...assuming my first bash at the tex comes out it says to transfer it into polar form and evaluate it i have no idea how to convert a limit of infinity to polar form, help...

I'm having trouble with this question. It's from Rindler's Introduction to Special Relativity which I'm going through myself. I'm just starting to learn about tensors. <<<<i) A vector A^i has components \dot{x}, \dot{y} in rectangular Cartesian coordinates; what are its components in polar...

Hello, I have this complex number that I need to convert to polar coord represntation: z = 1 + j; the answer is sqrt(2)e^-j45 (45 is degrees). The part I don't undestand is negative before j45, since a and b are positive, I assumed it's in the first quandrant of Im/Re plane, and if the...