It follows that the intersections of those curves are the points where Re(f(x)) = Im(f(x)) = 0, which means they are the roots of the equation f(x) = 0. Solve Equations in Mathematica using Solve, FindRoot and Reduce Hifas Faiz 1. The cross-sections of the two surfaces by the horizontal plane c = 0 are pairs of curves where each function is zero, respectively. There are two principle tools for finding roots of polynomial equations in Mathematica : Solve > generates analytical expressions for the. For example, f(x) has the following graphs for the real and imaginary parts. Such functions can be plotted in 3D by representing x = a + i b as a point in the (a, b) plane, and the value of the function along the third dimension, say c. So my question is: is it possible to identify the roots of such an equation by simply looking at the real and imaginary parts of the plot?į(x) = x^2 - 1 + i (x^2 - 0.5) is a complex function of a complex variable, which maps a complex variable x = a + i b to the complex value f(x) = Re(f(x)) + i Im(f(x)).Įach of Re(f(x)) and Im(f(x)) is a real function of a complex variable. However, this equation has no real roots, so the crossing points are different. If they both crossed the horizontal axis at the same point(s), that would mean the equation has real root(s), since both real and imaginary parts would be zero for some real value of x.
Those are graphs of the real and imaginary parts plotted for real values of x. We have a real part which crosses zero, and an imaginary part which also crosses zero but at a different x.
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