Can someone give a physical meaning for imaginary numbers? The imaginary numbers, in my opinion, are truly imaginary. What do they even represent? Irrational numbers are, well, preposterous but I can accept them. √2, π and φ have some tangible meaning, but √(-1)? What does it mean? A solution of x^2+1=0? But that equation itself is artificial, representing nothing physical, at least as of now. Complex numbers represent vectors and are useful as phasors in electrical engineering, electromagnetism and other fields. But that is all they are – a tool, a short hand notation to ease the mathematical calculations – and not really real. Phasors allay the complexity of calculations but even without them we could still do all the calculations, albeit in a convoluted way. So do these imaginary numbers mean something in reality? Can someone give me an example? The closest real world counterparts of complex number I can think of are the probability amplitudes of quantum physics.