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- == Polar form for complex numbers == The polar form for [[complex number]]s allows us to graph complex numbers given an [[633 bytes (105 words) - 12:35, 1 April 2022
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- '''Cis''' notation is a [[polar form | polar]] notation for [[complex number]]s. For all complex numbers <math>z</math>, * [[Polar form]]1 KB (171 words) - 19:59, 11 July 2023
- == Polar form for complex numbers == The polar form for [[complex number]]s allows us to graph complex numbers given an [[633 bytes (105 words) - 12:35, 1 April 2022
- Now, we can convert everything to [[polar form]] by letting <math>x = re^{i\theta} </math>, and noting that <math>1 =3 KB (558 words) - 20:36, 11 December 2011
- ...at the point as <math>(a,b)</math>. We can convert <math>z</math> into [[polar form]] and re-write it as <math>z=r(\cos\theta+i\sin\theta)=r cis\theta</ma1 KB (238 words) - 21:51, 20 February 2022
- === Solution 3.1 (Polar Form) === We rewrite <math>N</math> to the polar form <cmath>N=r(\cos\theta+i\sin\theta)=r\operatorname{cis}\theta,</cmath>7 KB (965 words) - 22:39, 11 September 2024
- The matrix for a reflection about the polar line <math>\theta = \alpha, \alpha+\pi</math> is: ...an 2</math>. Note that the line of reflection, <math>y = 2x</math>, is the polar line <math>\theta = \alpha, \alpha+\pi</math>. Then <math>2\alpha = \arctan4 KB (700 words) - 16:21, 3 May 2021
- The line is of equation <math>y=mx+3</math>. Substituting in the polar coordinates, we have <math>b_k = ma_k + 3</math>.2 KB (422 words) - 23:22, 5 September 2020
- The values in polar form will be <math>(1, 20x)</math> and <math>(1, 7.5x)</math>. Multiplying3 KB (564 words) - 03:47, 4 August 2023
- 2. Consider that the circles can be converted into polar coordinates, and their equations are <math>r = 40sin\theta</math> and <math2 KB (323 words) - 11:05, 16 July 2019
- In polar form, the solution to this polynomial can be expressed as <math>\cos \left(2 KB (343 words) - 05:20, 25 November 2007
- (b) Describe the circle as the curve <math>r = 1</math> in polar coordinates. We will construct a set <math>S</math> with an arbitrary numbe2 KB (460 words) - 12:35, 9 June 2011
- ...mathematical fields of [[complex numbers]]. It allows complex numbers in [[polar form]] to be easily raised to certain powers. It states that for <math>x\in2 KB (346 words) - 09:49, 31 August 2024
- ...e pair in Asymptote. There are two useful functions that allow one to use polar coordinates as well:7 KB (1,205 words) - 20:38, 26 March 2024
- Rewriting the [[complex number]]s in polar notation form, <math>1+i = \sqrt{2}\,\text{cis}\,\frac{\pi}{4}</math> and <1,008 bytes (141 words) - 20:13, 2 April 2008
- ...e the line parallel to the imaginary axis <math>x=\frac{1}{2}</math> using polar coordinates as <math>r(\theta)=\dfrac{1}{2\cos{\theta}},</math>6 KB (894 words) - 17:56, 25 December 2022
- First, turn <math>\frac34 + \frac34i</math> into polar form as <math>\frac{3\sqrt{2}}{4}e^{\frac{\pi}{4}i}</math>. Restated using2 KB (422 words) - 12:25, 20 January 2020
- ...any quadrilateral inscribed in the circle <math>\omega</math> meet on the polar line of the intersection of the diagonals with respect to <math>\omega \imp5 KB (792 words) - 00:52, 19 November 2023
- Now we have a solution at <math>\frac{n\pi}{4}</math> if we look at them in polar coordinate, further more, the 8-gon is symmetric (it is an equilateral octa2 KB (344 words) - 17:12, 22 August 2021
- ==Solution 6 (polar coordinates)== ...ould like to maximize <math>3x+4y,</math> we parameterize the circle using polar coordinates:9 KB (1,449 words) - 21:06, 6 December 2024
- ...the circle an orientation (e.g., letting the circle be the unit circle in polar coordinates). Then, for any set of six points chosen on the circle, there2 KB (297 words) - 21:29, 17 July 2016