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complex-numbers; Share. Cite. Follow asked Aug 27, 2013 at 2:19. Johnny Apple Johnny Apple. 4,471 2 2 gold ...
13 kwi 2014 · complex-numbers; Share. Cite. Follow edited May 23, 2018 at 15:36. Lorenzo B. 2,250 2 2 gold ...
3 lis 2010 · What are the three cube roots of -1? Not sure if this is a trick question, But I have been asked this. one of the ansers is -1, what are the other 2?
14 maj 2016 · Also, you keep losing nice properties. Passing from the reals to the complex numbers, we lose order; going from the complexes to the quaternions, we lose commutativity of multiplication. If we keep going, we lose associativity of multiplication, in increasing degrees: the sedenions are even less associative than the octonions, etc.
18 lut 2013 · Each complex number is assigned a magnitude and an angle (called the argument). This is done precisely with the complex exponential. You may recall that multiplying two complex numbers is equivalent to rotating one number by the angle of the second (and then applying the proper stretches and compressions).
If you understand Argand diagrams (the representation of complex numbers in the complex plane) and can envision the unit circle in it, you can easily do this in your head: -1 is 1 rotated over $\pi$ radians.
Since complex number field $\mathbb{C}$ is algebraically closed, every polynomials with complex coefficients have linear polynomial decomposition. In this case, it's $$ z^3 - 3z^2 + 6z - 4 = (z - 1)(z - 1 + \sqrt{3}i)(z - 1 - \sqrt{3}i). $$ So you can see the solution of the equation easily from this representation.
24 sty 2013 · That's complex numbers -- they allow an "extra dimension" of calculation. (Yes, I know about phase shifts and Fourier transforms, but these are 8th graders, and for comprehensive testing, they're required to know a real world application of complex numbers, but not the details of how or why. I don't understand this, but that's the way it is)
20 gru 2020 · However, if the variable can be complex, and entirely new vista of problems and possibilities opens up, and you shouldn't try to generalize your knowledge of real definite integrals to that setting without a course in complex analysis.
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