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What does a complex root signify? - Mathematics Stack Exchange A complex root of a polynomial can have some significance itself when the roots of the polynomial have significance in general One example that comes to mind where the roots of polynomials have a meaningful interpretation is in the field of dynamical systems
Graphically solving for complex roots -- how to visualize? We can present complex roots to equation on the "complex plane" with one axis for the real part and the other for the imaginary part You can play with, for instance, WolframAlpha, to give it a polynomial equation to solve and get a display of the complex roots If you look up "DeMoivre's Theorem" online, you will find something interesting about the roots of equations $ \ z^n \ = \ c
Is there an intuitive way of visualising complex roots? The axis of symmetry is the real part of the complex roots; the imaginary part can be found by subtracting the square of the axis (here, $4$) from the intercept ($13-4=9$) and then taking the square root ($3$) This assumes the roots come in conjugate pairs (so the coefficients of your quadratic are real numbers)
Explaining the nature of complex roots of a quartic Thank you for this I think I will start by demonstrating the distributive and commutative properties of the complex conjugate, then using those to state that if a complex numbers is a root of a polynomial, so is its conjugate, and therefore complex roots must come in conjugate pairs Then I can just list the cases for each order polynomial
complex numbers - What is $\sqrt {i}$? - Mathematics Stack Exchange The square root of i is (1 + i) sqrt (2) [Try it out my multiplying it by itself ] It has no special notation beyond other complex numbers; in my discipline, at least, it comes up about half as often as the square root of 2 does --- that is, it isn't rare, but it arises only because of our prejudice for things which can be expressed using small integers
Cubic with complex roots - Mathematics Stack Exchange 0 When I tried to solve the given cubic equation I found that it has three REAL roots as hereunder: -1 532089, 1 8793852 and -0 3472962 Since you have mentioned that the equation has complex roots I tried to put the above values in the equation and found that the equation is satisfied with each value
Complex roots of real polynomials and real roots of their derivatives Applied to quartic equations with two sets of complex conjugate roots, the theorem implies that in general the roots of the quartic are at the vertices of a quadrilateral in the complex plane and the roots of the derivative (real and otherwise) lie inside this quadrilateral