Graphical interpretation and visualizing the Complex Roots of Transcendental functions with Real Coefficients (New version). 1
Enter the values of the coefficients a and b of the Transcendental function and find its Roots.
Graphical interpretation the Roots: the intersection of implicit functions, which are the zeroed real and imaginary parts of the complex function f(z), respectively: real(f(z))=0 and imaginary(f(z))=0.
Point z0' of intersection of the considered curves is found (using the CAS) solution of the system of two equations of these curves. The starting point is the moving point z0. At this complex point, obviously, there should be f(z0')=0.
There are 9 moving test complex numbers lz={z1, z2,...,z9} that can be placed "approximately" at the intersection points of the considered curves. By sequentially pressing the button "SetValue[j,j+1]", these settings are refined by solving the corresponding equations in CAS. In the table you can see these 9 complex numbers and see how accurate they are as the roots of the equation f(z). Make sure that in these cases all f(zi)=0 are at the origin.
In this version of the applet (unlike the previous one), the point of intersection of the curves is found by numerical methods with a high degree of accuracy.
More complicated view of the function is in the applet .