Complex numbers and the complexity of life.

Sometimes I wish I could go back to when I was younger. I mean life was simpler then. I remember seeing a meme on facebook saying "don't grow up, it's a trap". I think it is...lol. Growing up comes with some challenges and some life's "curve balls". Well, maybe not for everyone, let me not be a spokesperson of "everybody". But that's where the "complexity" of life knocks in. The complexity is relative, of course, with everyone.

Some few weeks ago we had our revision lecture, which was basically the last lecture of the year, for MATH1034, an Algebra course for first-year students. Last lectures, especially those before exams, have a mixed "aura". The students are relieved that it's the last lecture, others are jubilant while others are worried of what's coming in the exams. However, as always, we had fun during the lecture - it was the last lecture, why not?

One of the concepts we were doing for revision was complex numbers. I remember when I first heard of the phrase "complex numbers", I was expecting some really complex thing. Some of my students still argue that complex numbers are complex. A complex number is of the form z = x + iy where x and y are real numbers and "i" is the square root of -1. You see,...nothing complex, but "i" being the square root of -1 can be complex to comprehend at first. For terminology we call x the real part and y the imaginary part of the complex number z.

I have this thing of always trying to relate every concept I lecture to everyday life. I do this even when I study mathematics, funny enough, but it was further reinforced by the questions students posed during lectures. I used to lecture mathematics to engineering students and the questions they used to ask, yooohh. They will be like "Sir, we see all the mathematics and all that but where will we apply this in real-life?" I get it, engineering is a technical discipline.

So as I'm lecturing on these complex numbers I turn around and be like "yeah, life is so complex neh". The facially expression of the students were like "and then?" Remember a complex number is made of the real part and an imaginary part, I actually find life to be like that. The real part of life is the things that are happening in real-time or in reality, some can say the tangible staff (but even some of the intangibles can be viewed as being real). I guess everyone has their definition of reality. You also have the imaginary part of life, some would say the imaginary world - this is where we imagine things. I find the imaginary world to be a nice place to be in, this is where our dreams, ambitions, goals, etc, are - everything is possible in the imaginary world. I remember when I was still in first-year, I would imagine then that in four years time (assuming then that I would graduate in four years) I will be driving my dream car, living in my dream house, married to my dream woman and having the coolest and cutest kids. Oho, I'm still here...laugh with me, lol. What I'm saying is that my imaginations didn't meet my reality for that time frame. I think there's a conflict, a conflict with "self", when the imaginary parts of our life (the things we imagine) don't match the real-part of our lives (doesn't match our reality). I call that conflict "the complexity of life". Well, that complexity is of course relative, there might be some things more complex than that. In my life perspective I find the complex things in life being the things that which the juxtaposition of their reality (real-part) and imaginations (imaginary-part) are not that trivial. For example, some students find geometry to be complex because with geometry your mind must be able, to some degree, to perfectly imagine those geometric shapes. Failure to do so can be the beginning of misunderstanding geometry. Thus for geometry your mind must move back and forth from being imaginative to being real. I found that to be the same when I was studying astronomy. I argue that the same goes with abstract mathematics. Another concept which in my opinion is complex, at least for me, is spirituality (depending on what you believe in) because the "spiritual realm" is imaginative particularly because it is to some extent intangible, but it must manifest in reality. So, based on that, spirituality has an imaginary part and a real part, which makes spirituality some form of a complex number. This sounds like fiction now, lol.

My submission is the "complexity" of life is the imbalance between its real-part and its imaginary part. At least that's the complexity I'm referring to here as there might be other complexities. I'm cautious when I say this because I sometimes get into debates with philosophy students. Life, as I perceive it, consist of its real part (reality) and its imaginary part (imaginations, dreams, ambitions, etc), and for that, it conforms to complex numbers and hence its complexity. I know I sound so philosophical on this one...look at me now, lol.

I said all of the above while lecturing the students on complex numbers. At that moment the lecture got so philosophical and "evangelistic". Some students interjected with "halelluya" and some with "preach man of God, go deeper". It was funny! In the previous year I had this student who was a Sol-Phenduka-kind-of-a-person (if you're a chiller you know) who, after the lecture on complex numbers, said that his relationship status is complex because he doesn't have a real girlfriend but have an imaginary girlfriend. If you understand complex numbers you should get the pun. I hope it's not complex!

Yours complex(ley)

Ben Mahudu.