Complex Numbers & Dreams - 1

Good evening people,

Today was a bit different from the other days. I got some time to fill this space pretty early, and I want to talk about Complex Numbers. The title of this post might sound goofy, but I had been thiking over this for the past couple of years. As a matter of fact, Complex Numbers were born after the discovery of the imaginary number  -- sqrt(-1) denoted as "i".

These numbers cannot be represented on the normal x,y co-ordinate plane, and yes these have the imaginary part, just as we do have imaginations. Couple of days ago, I was solving a linear ODE system using matrices. Normally when the eigen values of such systems are calculated they turn out to be distinct, which would facilitate the method to discover the eigen vetors and solve the problem. However, for that particular system, the eigen values turned out to be complex numbers in some particular cases. However, the given physical system was not imaginary. Hope you are following me...Let me rephrase my sentences. I was solving the equations of a reactor which is physically existing and running perfectly, however I encountered imaginary values, as I tried to solve those equations. Technically, this should not happen  as the given system is real.

Nevertheless, I tried to solve the problem with the obtained imaginary numbers, and thanks to De Moivre for his wonderful theorem, {exp(it) = cost + isint}, which converts these complex numbers to trigonometric functions. After that step, the usual Gaussian Elimination, finally me the result which was surprisingly a real value. I was full of joy after solving the problem, but....

What happened to the imaginary eigen value numbers?

Why were they eliminated at the end??

How would that happen???

Doesnt it look similar to the dreams which vanish as soon as we wake up from sleep??  Are dreams really imaginary??  or  imaginarily real??

These questions were born in my mind, and I guess you would have the same questions in your mind too...

I would take a leave here today, and would talk about it tomorrow, as i got some Non-Linear ODE stuff to work on right now. Hope you would share your thoughts on this post.

See you people tommorow.

Let peace prevail in this world.

--

Sun.