Choose the Coeffitiants a and b and the corresponding exponents exp1 and exp2 as well and the absolute part c to generate a complex function. Or just hit the Random-Button. Then use the slider for r (=|z|) to change the absolute value of z to see how the graph of f(z) changes. The dashed circle is the path z moves on. The other line is the path z' moves on. Notice that it passes through the origin and collapses to the value of c! Try to hit the origin and you have found a root! (Well, kind of.) (You can use Shift and drag to move around.)

(c) 2014 Robin Koch Inspired by Numberphile [url]https://www.youtube.com/watch?v=shEk8sz1oOw[/url]