Monday, March 23, 2009

Complex Analysis

It must have been around the fifth semester and the course was an elective called Complex Numbers.

Now a guy like me needs a course that started with Complex as badly as a praying mantis needs a lesson in table manners. Simple Sums, Easy Arithmetic Tricks, Summies for Dummies—any of these would have put me on a fast track towards a ten-point-oh, but they never appeared on the menu. So I missed out.

Actually, I think I suffered from an undiagnosed ailment that philosophers call prospective distortion. This is where you assess matters with grossly misplaced optimism before disaster strikes you down. It often repeats. It afflicted me whenever I made course selections at the rosy beginning of each semester. This kind of optimism would have been perfect on Wall Street.

But let’s make it back to the story. The professor handling complex variables was Raghava Rao—a metronomic character whose pedagogical method was the art of rote that he had effectively demonstrated at the introductory math courses. He would rewrite dense and archaic Piskunov formulations and explain them monotonically to the blackboard. You were left to work with the rebound.

Raghava Rao did his roll call at the beginning of each class. The accidental convenience of this arrangement allowed you to sneak out anytime after the roll call—for a bathroom break, or any other excursion of your choice from which you weren't compelled to ever return. The roll call would continue ponderously for the first ten minutes. Swimshake, VizaiYes, AnoozeBee would provoke consecutive YesSirs from Suheim Sheikh, me and Anuj Bellare, moments before Suheim and I would contemplate the break for freedom.

It was exam day in complex numbers. The question paper had been distributed and the silence was punctuated by the occasional rustle of paper. Sitting close to me was Amar, punching furiously at his calculator.


Now let me tell you that when dealing with complex numbers, a blow torch would come in handier than a calculator. Complex numbers is all theory stuff and you’ve got to get your head wired up to imagine imaginary parts, even as you lost the handle on the real ones. I may remember nothing about the course, but I can proudly tell you that Euler figured out that cos theta plus i sin theta equals e raised to i theta.

I later found out that even Euler had to stand on his head for three whole days, before he could coax this one out of his upturned brain.

Raghava Rao comes over to Amar to investigate the deployment of the said calculator and this is what he beholds.

Amar takes a number, raises it to the power of zero, and avidly checks the result: One. He tries it again with another number: One. And another: One. Since three appeared to make for adequate proof, he delves back into his paper, notes something down and resumes the test.

The unflappable Raghava Rao is, for once, aghast. He comes up to the front of the class and interrupts the test with this stinging announcement.

“There must be something wrong with me”, he says. “It can only be my fault. I just saw one of your classmates checking the zeroth power of several numbers on his calculator. This is the final exam in complex variables and if this is what you have grasped, I must have done something wrong.”

All this from a man who has never addressed the class during the academic year.

Later that evening at the hostel, I ask Amar what had possessed him. “Obviously I knew the result, da”, he says with nonchalance, “I was just checking it. What’s Raghava Rao’s problem, anyway?”

I think philosophers call this one retrospective penitence.


  1. Wow! I was equally cavalier with my instructors, but this one takes the cake - what was that guy Amar thinking?

  2. Ha, ha! Very funny. I can just picture Amar doing that.

  3. PS. Complex Variables -- I seem to remember that was what it was called -- was one of the few courses I really enjoyed (and remembered quite a bit about well after I had left IIT).