[size=85]Enter the values of the coefficients [b]a[/b] and [b]b[/b] of the [b][i]Transcendental function[/i][/b] and find its [b][color=#333333]Roots[/color][/b]. [br] [i]Graphical interpretation the [b]Roots[/b][/i]: the [i]intersection of implicit functions[/i], which are the zeroed real and imaginary parts of the complex function [b]f(z)[/b], respectively: real(f(z))=0 and imaginary(f(z))=0.[br] In the general case, these roots can be found numerically. Here, you can set the function f(x). Using 9 test points [b][color=#ff0000]z[sub]i[/sub][/color][/b], approximately find its [b]roots[/b] by moving them to the intersection points of the [i]implicit functions[/i] under consideration, and make sure that in these cases [b][color=#ff0000]fz[sub]i[/sub]=f(z[sub]i[/sub])[/color][/b] is at the origin, i.e. [b]z[sub]i[/sub][/b] are the [b]roots[/b] of the original equation. The roots and function values for them are shown in the table.[br] The [b][color=#ff0000]z[sub]8 [/sub][/color][/b][color=#333333]and[/color] [b][color=#ff0000]z[sub]9[/sub] [/color][/b]complex numbers are at the intersection of the considered implicit functions. However, they are not the roots of the equation: f([color=#ff0000][b]z[sub]8[/sub][/b][/color])≠0 and f([color=#ff0000][b]z[sub]9[/sub][/b][/color])≠0!? Either the graphical representation of the implicit functions is not accurate, or... The gradients of both functions at these points are very large and a great precision of calculating the intersection points is required: Points on the "[i][color=#dd7e6b]real[/color][/i]" and "[i][color=#1e84cc]imaginary[/color][/i]" curves, respectively Point([b]eq[sub]a[/sub][/b]) and Point([b]eq[sub]b[/sub][/b]) near [b][color=#ff0000]z[sub]8[/sub][/color][/b](or [b][color=#ff0000]z[sub]9[/sub][/color][/b]),[i] nullify[/i] these [i]equations[/i]![br] Another example can be found in the applet https://www.geogebra.org/material/show/id/gamqfzzw[br]*New [url=https://www.geogebra.org/m/spsahker]version[/url] available.[/size]