Question

If all the measurements in science are real...why should we need complex numbers.(which has an imaginary part in it..) does it have any physical sense...?

Answer 1

Electrical engineers who deal with power systems use complex numbers. Instead of i, they use j since i is used to designate current.

AC circuits have resistance and reactance. R and X. The sum of these two complex numbers is impedance, Z.

Answer 2

This is a very important question. As far as I'm aware you don't see complex numbers in classical mechanics. When I say classical, I mean physics before the advent of Quantum mechanics. The reason why complex numbers don't appear in classical calculations is because we treat particles as point-like, which in principle have well defined positions and momentum and it turns out that real numbers are enough to describe the physics.

On the other hand quantum mechanics says that particles are described by a wave function which in a lot of cases is complex and that particles can not have simultaneously well defined positions and momentums.

All we can do is assign probabilities to these quantities. Now probabiliites are found by calculating amplitudes of the wave function which is done by first multiplying the wave function with its complex conjugate (which is a real number).

So although the wave function itself is not a "physical" quantity (this is the current belief) the square of the wavefunction is.

Answer 3

In short, complex numbers are a very useful tool as part of the way we calculate things. Even in classical physics, it's very useful to have them as they enable a more rapid way to solve certain types of equations and they also provide a compact way to describe certain types of wave motion.

The claim of Physics in using complex number is not that there are quantities in the work that are "complex valued"; rather, it is just that mathematics involving complex numbers giving us working models that can usefully and reliably predict things. And that is the best sort of claim any scientific theory and its tools can make.

Answer 4

There is a difference between what actually happens and what mathematical models predict will happen. Part of the goal of science is to make them as similar as possible, but in the end, math is just a creation of man to help us understand what we don't.

Answer 5

Actually we need complex numbers in order to simplify our theoretical computations in physics.If we choose the real system our problem solving processes can be really tricy whereas in many complicated problems in physics we choose to first convert the problem in complex sysytem then solve it using the complex algebra and physics rules very easily and then at last extract our desired real result from the complex answer.....this is the whole recipe.....u can very easily see this in circuit analysis in electricity and magnetism..