Polar form Definition and 101 Threads

In the following%3A%20https://pubs.rsc.org/en/content/articlehtml/2013/sm/c3sm00140g?casa_token=3O_jwMdswQQAAAAA%3AaSRtvg3XUHSnUwFKEDo01etmudxmMm8lcU4dIUSkJ52Hzitv2c_RSQJYsoHE1Bm2ubZ3sdt6mq5S-w'] paper, the surface velocity for a moving, spherical particle is given as (eq 1)...

The equation I'm trying to graph on desmos is this with A & B as numbers, but I'm unsure how as it is a vector. r = (A cosθ sinθ cscθ - B sinθ cscθ) i + (A cosθ sinθ cscθ + B sinθ cscθ) j

Hello, Today I started to think about why graphs, of the same equation, look different on the Cartesian plane vs. the polar grid. I have this visualization where every point on the cartesian plane gets mapped to a point on the polar grid through a transformation of the grids themselves...

Summary:: Hello, my question asks if the complex exponential equation 4e^(-j) is equal to 4 ∠-180°. I tried to use polar/rectangular conversions: a+bj=c∠θ with c=(√a^2 +b^2) and θ=tan^(-1)[b/a] 4e^(-j)=4 ∠-180° c=4, 4=(√a^2 +b^2) solving for a : a=(√16-b^2) θ=tan^(-1)[b/a]= -1 b/(√16-b^2)=...

Express -3-3i in polar form. I know that r=3√2. And I understand that now we take tan^-1(b/a) which I did. tan^-1(-3/-3) = π/4. So I put my answer as z = 3√2 [cos(π/4) + isin(π/4)]. However the answer manual told me this was incorrect I am unsure of where I went wrong...

I don't fully understand how to work out the impedance from the given equation (5j-5)x(11j-11)/(5j-5)+(11j-11). Any help would be greatly appreciated. Thanks. The answer needs to be in rectangular and polar form.

Homework Statement Write ##5-3i## in the polar form ##re^\left(i\theta\right)##. Homework Equations $$ |z|=\sqrt {a^2+b^2} $$ The Attempt at a Solution First I've found the absolute value of ##z##: $$ |z|=\sqrt {5^2+3^2}=\sqrt {34} $$. Next, I've found $$ \sin(\theta) = \frac {-3} {\sqrt...

x^2+y^2=4 I have so far: (r^2)cos^(theta)+(r^2)sin(theta)=4 Idk what I'm supposed to do from here

Convert the equation to polar form 8x=8y I thought it would be 8*r*cos(theta)=8*r*sin(theta) Said it was incorrect then I thought I needed to divide by 8 to remove it, giving me: r*cos(theta)=r*sin(theta) But that was also incorrect and now I am stuck

Hi, I am going around in circles, excuse the pun, with phasors, complex exponentials, I&Q and polar form... 1. A cos (ωt+Φ) = Acos(Φ) cos(ωt) - Asin(Φ)sin(ωt) Right hand side is polar form ... left hand side is in cartesian (rectangular) form via a trignometric identity? 2. But then...

Homework Statement It's not a homework problem itself, but rather a general method that I imagine is similar to homework. For a given elementary complex function in the form of the product, sum or quotient of polynomials, there are conventional methods for converting them to polar form. The...

Hi, I had a question I was working on a while back, and whilst I got the correct answer for it, I was told that there was a second solution to it that I missed. Here is the question. ] I worked my answer out to be sqrt(2)(cos(75)+i(sin(75))), however, it appears there is a second solution...

How is this done? My textbook only specifies integrating polar graphs with respect to theta.

Hello everyone, I have a complex number problem that i would greatly appreciate some help with. Thanks in advance to anyone offering their time to make a contribution. Q) Write the following in polar form: I have attempted the question (please see my working below) and have been advised that i...

Homework Statement you are given the standard form z = 3 - 3i Homework EquationsThe Attempt at a Solution so to convert this to polar form, i know that ##r = 3√2## but how do i find theta here? There are so many mixed answers it seems online that I can't tell... i know that ##(3,-3)## is in...

Homework Statement well this is not exactly a homework, i had an argument whith my teacher about my grade in a test, because i put a complex number in the form of R,theta and she claims that the form was costheta+isentheta, and i know that but i need to prove in a book that...

Hi all, I was doing some math and I stumbled upon a very interesting thing. When I do ln(-1), I get πi, and when I turn that into polar coordinates on the calculator, it gives me πeiπ/2 . Why is that? I'm very curious to know, because they are so intertwined! Thank you

Homework Statement Homework Equations r=sqrt(a^2+b^2) θ=arg(z) tan(θ)=b/a The Attempt at a Solution for a)[/B] finding the polar form: r=sqrt(-3^2+(-4)^2)=sqrt(7) θ=arg(z) tan(θ)=-4/-3 = 53.13 ° 300-53.13=306.87° -3-j4=sqrt(7)*(cos(306.87+j306.87) I don't know if my answer is correct...

Homework Statement \frac{z-1}{z+1}=i I found the cartesian form, z = i, but how do I turn it into polar form?The Attempt at a Solution |z|=\sqrt{0^2+1^2}=1 \theta=arctan\frac{b}{a}=arctan\frac{1}{0} Is the solution then that is not possible to convert it to polar form?

Homework Statement can someone explain about the formula of the circled part? Why dA will become r(dr)(dθ)? Homework EquationsThe Attempt at a Solution A = pi(r^2) dA will become 2(pi)(r)(dr) ? why did 2(pi) didnt appear in the equation ?

$$y=\sin\left({x}\right) $$ write in polar form This reduces to $$r=1$$ So that's not = plots Not sure why I can't get these simple equations

$y=x^3$ in polar form I got to this but it didn't plot ${x}^{3}$ $$r=\pm\sqrt{\frac{\sin\left({x}\right)}{\cos^3\left({x}\right)}}$$

Homework Statement I have the following complex numbers : -3,18 +4,19i I must put it in polar form. Homework Equations r=(a^2+b^2)^(1/2) cos x = a/r sin x = b/r The Attempt at a Solution I was able to find with cos x = a/r that the x = 127,20 But when I do it with sin x = b/r I obtain like...

Homework Statement A lamina has constant density \rho and takes the shape of a disk with center the origin and radius R. Use Newton's Law of Gravitation to show that the magnitude of the force of attraction that the lamina exerts on a body of mass m located at the point (0,0,d) on the positive...

Hello Excuse me, but how do I sketch the phasor of a voltage that it's V=5cos(10t+30degrees) and how the V=5sin(10t+30degrees) ? I know that these can be converted as the R<angle polar form, with R being the Vmax, ie the 5, and the angle the phase. But what doesn't it matter if I have cos or...

Greetings. I have been teaching myself Calculus. To do this I ordered a used Larson's 8th Edition Calculus and a used TI-81 graphing calculator. When I got to Chapter 10, I ran into a problem: the chapter introduces equations in polar form and when I whipped out my TI-81, I had no idea how to...

Homework Statement "Put each of the following into the form Acos(ωt+θ)..." (a.) 4ejt+4e-jt Homework Equations Euler's Identity: ejθ = cos(θ)+jsin(θ) Phasor Analysis(?): Mcos(ωt+θ) ←→ Mejθ j = ej π/2 Trignometric Identities The Attempt at a Solution I attempted to use phasor analysis to...

another question: convert $|\frac{1-i}{3}|$ to polar form i am getting $\frac{\sqrt{2}}{3} e^{\frac{i\pi}{4}}$ but the solutions say: $e^{\frac{-i\pi}{4}}$ i did $ x = r\cos(\theta)$ and $y=r\sin(\theta)$ so $\frac{1}{3} = {\frac{\sqrt{2}}{3}}\cos(\theta)$ $\frac{1}{3} = \cos(\theta)$ And...

I started of with attempting to convert the numerator first $ | 1 + i | = \sqrt{1^2+i^2}$ $= \sqrt{1-1} = 0$ ? this is wrong obviously, i don't see why its $\sqrt{2}$ for the second part $ |\sqrt{3} - i|= \sqrt{3+1} = 2$ $ x = r \cos\theta$ $ y = r\sin\theta$ $x = 2\cos\theta$ $...

Homework Statement Hello Guys, I am reading Hobson's General Relativity and I have come across an exercise problem, part of which frustrates me: 3.20 (P. 91) In the 2-space with line element ds^2=\frac{dr^{2}+r^{2}d\theta^{2}}{r^{2}-a^{2}}-\frac{r^{2}dr^{2}}{{(r^{2}-a^{2})}^{2}} and...

Homework Statement A 90Ω resistor, a 32 mH inductor, and a 5μF capacitor are connected in series across the terminals of a sinusoidal voltage source Vs = 750cos(5000t + 30)V. Calculate the phasor current. Homework Equations phasor current i = V/Z V in polar form = (Magnitude)(cos a + j sin...

Homework Statement 4{cos(13∏/6)+isin(13∏/6)} = 4((√3/2)+(i/2)) = 2√3+2i Homework Equations The Attempt at a Solution This is an example from my textbook. The part which I do not understand is how to convert the cos and sin of radians into those fractions. Any help is greatly appreciated.

Homework Statement Find the polar form for zw by first putting z and w into polar form. z=2√3-2i, w= -1+i Homework Equations Tan-1(-√3/3)= 5∏/6 The Attempt at a Solution r= √[(2√3)2+(-2)2]=4 tanθ= -2/(2√3)=-1/√3=-√3/3=> acording to above... tan-1(-√3/3)= 5∏/6 so, in polar form z should be...

Homework Statement How do I write 1-2i in polar form? Homework Equations The Attempt at a Solution I know r=√5, and when using x=rcosθ, I get angle of 63.43 or 296.57. However, when I take the sin inverse of-2/√5 I get -63.43. I am really confused.

Homework Statement \int_0^2 \int_0^\sqrt{2x-x^2} xy,dy,dx I know the answer, but how does the 2 in the outer integral become pi/2?? I'm fine with everything else, I just can't get this...

Homework Statement An impedance 8 + j7 Ω is connected in parallel with another impedance of 5 + j6 Ω. this circuit is then connected in series with another impedance, comprising a resistance of 5 Ω in series with a capacitive reactance of 7 Ω. The complete circuit is then connected to 150...

the question is showed below i know that x=rcos θ and y= rsinθ and x^2 + y^2 = R^2 but i just dun know how to find the locus is polar form any clue ?

Homework Statement Write z = 1 + √3i in polar form Homework Equations z = r (cos\varphi + sin\varphii) The Attempt at a Solution Found the modulus by |z| = √4 = 2 Now I am stuck on this part of finding the argument: Tan-1 (√3) now I am not sure how to go from that to...

Hi all, There is a question that asks? Determine the cube roots of 1 in polar form? Does that mean I can use De Moirve Formula? Stephen

Homework Statement Write the equation x^2 + y^2 = 1 + sin^2(xy) in polar form assuming x = rcos(\phi) y = rsin(\phi) 0<r, 0<= \phi < 2pi solve for r as a function of \phi The Attempt at a Solution (rcos(\phi))^2 + (rsin(\phi))^2 = 1 + sin^2(r^2cos(\phi)sin(\phi))...

Not homework as such, just need some clarification. When finding \alpha do you have to take the signs into account when finding tan^{-1} x/a. Does it matter if a or x are negative? Next question is about quadrants 1: \theta = \alpha 2: \theta = \pi - \alpha 3: \theta = -\pi -...

Homework Statement do you see how the integral of r is .5? I don't get how that follows?

I couldn't find any book discussing all of this. =================================================== U+jV=f(x+jy) W=f(z) Ux=Vy Uy= -Vx jWx=Wy <--Cauchy-Riemann equation Uxx+Uyy=0 Vxx+Vyy=0 <--harmonic condition...

Homework Statement Consider the complex number z=(i^201+i^8)/(i^3(1+i)^2). (a) Show that z can be expressed in the Cartesian form 1/2+(1/2)i. (b) Find the modulus of 4z − 2z*. (z* meaning z-bar/complex conjugate of z) (c) Write 2z in polar form. (d) Write 8z^3 in polar exponential form...

Homework Statement express the arg(z) and polar form of (1/\sqrt{2}) - (i/\sqrt{2}) Homework Equations The Attempt at a Solution Ok so I did \sqrt{(1/\sqrt{2})^{2}+(1/\sqrt{2})^{2}} = 1 so tan^{-1}(1) = \pi/4 so arg(z)=5\pi/4 but they had the answer as -3\pi/4 Am I...

Homework Statement Given that z_{1}z_{2} ≠ 0, use the polar form to prove that Re(z_{1}\bar{z}_{2}) = norm (z_{1}) * norm (z_{2}) \Leftrightarrow θ_{1} - θ_{2} = 2n∏, where n is an integer, θ_{1} = arg(z_{1}), and θ_{2} = arg(z_{2}). Also, \bar{z}_{2} is the conjugate of z_{2}. Homework...

Homework Statement I'm trying to find the best solution for solving a problem in which I must form an operation with three vectors in polar form, ending with a sum in rectangular form. The operation is as follows: (5 \angle 0°) + (20 \angle -90°) - (6 \angle180°) = Homework Equations...

Homework Statement Alright, here's the question, A stream function for a plane, irrotational, polar-coordinate flow is ψ=9r^2sin^θ. Find out the velocity potential in Cartesian Co-ordinate! Homework Equations The Attempt at a Solution Well, I can easily find out the velocity...

Hello, I'am new here and happy to find this great forum! Here's my first question: there's an explicit function as follows: y=2.sin(x)-1 The transformation to polar form (r=3cos(\theta)) - x=r.cos(\theta) - y=r.sin(\theta) So I get: r.sin(\theta)=2.sin(r.cos(\theta))-1 Now you see...

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...