Complex functions: Domain colouring with contour lines

Drag the grey point or slider. Change the function f(z). Example: (z-i)/(z+i)
Other functions to try:[br][list][*](z-1)/(z^2+i*z+i)[/*][*]exp(1/z)[/*][*]ln(z)[/*][*]z^3-1[/*][*](1-cos(z))/z^2[/*][/list]

Information: Complex functions: Domain colouring with contour lines