Everyone here knows $\sqrt{-1}$ is called the imaginary unit. If, suppose we are doing a calculation regarding a physical situation and some of the solutions at the end turn out to be "imaginary" and some are real then we reject the imaginary ones without even giving them a second thought $\textbf{just because they were imaginary}$ (at least I was told to do like this). But the other real solutions are given a thought about why we are rejecting them before rejecting all the ones not physically realizable.
Now, suppose we did not have given this name "imaginary" then people would surely have given at least some thought before rejecting them. One case where I encountered a "purely imaginary" (not complex) solution being accepted is in the calculation of spacetime interval in general relativity to classify them as space-like, time-like or null-like. It sure has a physical significance in GR. But, in general, how could we always say complex solutions solve no physical situation. Let me give you an example.
Say, we are calculating where will maximum bending occur in a simply supported beam given a force distribution on it. The beam is of length $5$ (from $x=0$ to $x=5$). And suppose we get solutions as $x=\{-1,\ 3,\ 1-i,\ 1+i\}$. From these solutions, we will reject $x=-1$ as it lies outside the beam but on what basis will we reject the complex solutions if they were not given the name "imaginary". The only reason I have to reject the complex solutions is that the solution $x=3$ solves the situation and my intuition (and practical work) tells me this is the only solution for this physical situation.
If someone could give me a different and satisfying way of thinking why we reject complex solutions (even if only in the case I used) would be really appreciated.
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