So, now that you have reviewed and clearly are a master at imaginary and complex numbers, are you ready to teach the other professors?  Some of them might learn a little differently than you or I do (they ARE mad scientists after all).  Can you please come up with a few new ideas on how to explain imaginary numbers and graphing complex numbers to those crazy few who do not get it the "normal" way?

Also, can you explain to them how imaginary and complex numbers differ from one another? How do they differ from real numbers? How are they similar?

Now, the smart alec in the back wants to know how can we solve negative square roots without imaginary numbers.  So, have you got a "real" answer for him or an "imaginary" one?