e to the power of whatever

On the right, change the value of k. On the left, is plotted. You can move the time slider yourself, or just press "start". The app is based on the lovely video by 3Blue1Brown, copied below; watch it first! (There are some tips below the video.)
  • Start by trying to recreate what Grant does in the video. Set k=1 then k=2 then k=-0.5 then k=i and note the change of behaviour between each.
  • Stop the animation and reset to t=0 before changing k so that you can see how the initial velocity changes. (Click "show velocity"!)
  • For k=i... try to stop time when . At what value of t does this occur?