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  • The '''complex numbers''' arise when we try to solve [[equation]]s such as <math> x^2 = -1 ...set of complex numbers is denoted by <math>\mathbb{C}</math>. The set of complex numbers contains the set <math>\mathbb{R}</math> of the [[real number]]s, s
    5 KB (860 words) - 14:36, 10 December 2023
  • The absolute value function exists among other contexts as well, including [[complex numbers]]. ==Complex numbers==
    2 KB (368 words) - 09:37, 5 January 2009
  • For any [[complex number]] <math> w=a+bi </math>, <math> |w| </math> is defined to be the [[r Finally, we can calculate the given modulus,
    4 KB (665 words) - 09:04, 8 September 2024
  • ...umber with <math>|z|=2014</math>. Let <math>P</math> be the polygon in the complex plane whose vertices are <math>z</math> and every <math>w</math> such that ...circle <math>O</math> with the origin as the center and radius 2014 on the complex plane. It is clear that <math>z</math> must be one of the points on this ci
    6 KB (1,045 words) - 12:08, 21 January 2024
  • ...<math>0, z,</math> and <math>z^3,</math> when represented by points in the complex plane, are the three distinct vertices of an equilateral triangle? Convert <math>z</math> and <math>z^3</math> into modulus-argument (polar) form, giving <math>z=r\text{cis}(\theta)</math> for some <
    7 KB (1,136 words) - 10:16, 30 October 2024
  • ==Solution 2 (Complex)== We place the ant at the origin of the complex plane with its first move being in the positive real direction. Then the a
    9 KB (1,380 words) - 15:12, 2 January 2024
  • ==Solution 5 (Complex)== ...nd rotations also don't affect the length (modulus or absolute value) of a complex number. This motivates us to set <math>z = \exp (i\theta)</math>, starting
    6 KB (916 words) - 10:19, 9 November 2024