Why imaginary co-ordinates and complex numbers?

[aditya23456]

Most of advance/modern physics has i(imaginary components like E and P are represented so ) in it..How does these imaginary co-ordinates or axes fit into application of physics which explains real world phenomenon..Hope my question sounds reasonable.?.THANK YOU IN ADAVANCE

 

[kurtlesker]

i believe imaginary coordinates are just convenient ways to express sinusoidal functions
e^(ix)=cosx +I*sinx .
There's this thing call Fourier series that says anything in the real world can be described by adding many sines and cosines together, so that's why many physicists choose to describe the world to describe the world with sines and cosines, and use these imaginary number exponentials to express these sines and cosines...

 

[homeomorphic]

Complex numbers are not removed from the physical world at all if you actually understand them. You can think of them as either points in a plane or amplitudes and phases of waves.

 

[genericusrnme]

They're handy for representing rotations.

That and the maths depends on it.
No 'physical observable' takes a complex value in QM, even if their operators are complex.

Things like the probability of something happening or an expectation value or whatever are the magnitude squared of a complex wavefunction usually, the magnitude of a complex number is a real number and so you don't get complex results for real physical observables.

 

[Khashishi]

I used to think of complex numbers as merely a useful trick and shorthand for two real numbers, and complex numbers were "artificial" whereas real numbers really existed in nature. Well, I have since changed my stance, and now regard all numbers as mere tools for human models, and this puts complex numbers and real numbers on more equal footing. In modern algebra, various kinds of numbers are not somethings that are discovered from nature, but rather somethings that are defined by their operations.

If complex numbers are more concise than real numbers for representing some theory, they are useful. Of course, any theory with complex numbers can be rewritten in real numbers only. It's silly to consider which representation is more "correct" if they both give the same results.

 

[nnnm4]

BUT, there is a note of technical importance. Exponentials are useful in representing real wave-like solution mainly if those solutions are of a linear equation of motion.