0

Complex number is very weird to me, especially so when they appear in engineering and physics equations.

It is possible to represent complex number as real matrix where $i = \begin{pmatrix} 0&1\\ -1&0 \end{pmatrix}$ and $1= I$

However, the eigenvalues and eigenvectors of the $i$-matrix are complex. Which means complex numbers may reappear even if we use the matrix representation.

Is it possible to totally get rid of complex number from our real world equations? Or is it so fundamental in our world?

somebody4
  • 227
  • 1
    they are equivalent to R^2, so it is messy but you can –  Feb 13 '19 at 11:48
  • Possible duplicates: https://physics.stackexchange.com/q/11396/2451 and links therein. – Qmechanic Feb 13 '19 at 11:57
  • 1
    You can't get rid of the fact that a polynomial of degree $n$ with real coefficients doesn't always have $n$ real roots, but a polynomial with complex coefficients does always have $n$ complex roots. In other words, you can get rid of complex numbers, but doing that is a complicated and untidy mess compared with keeping them. – alephzero Feb 13 '19 at 13:23
  • 1
    Re, "Complex number is very weird to me." That's the fault of your teachers. There are not many math educators who know (or will take the time to explain) the practical applications of complex numbers. Start by learning how complex multiplication relates to rotations in the complex plane. Then, learn what $\sin x$, $\cos x$, and $e^x$ mean in the complex world. (Hint: They're all solutions to the same differential equation.) Complex math simplifies the analysis of periodic functions, and wave phenomena. If you need help, seek an engineer or a physicist, not a math teacher. – Solomon Slow Feb 13 '19 at 15:11
  • Actually, thinking complex&real number as matrix rather then some mystical imaginary number make much more sense to me. Complex number arithmetic would be just some "degenerated" subset, a convenient tool. – somebody4 Feb 14 '19 at 02:04

0 Answers0