When solving a second order differential equation, and the characteristic equation has complex roots, are there situations where we would want to keep the solutions as complex rather than transforming...

When solving a second order differential equation, and the characteristic equation has complex roots,
are there situations
where we would want to keep the solutions as complex rather than transforming them into real solutions?

Note:   I have asked this question
two
other times and the solution provided is just an explanation of how to determine the real solutions.  That IS NOT my question.  I know that the general solution gives real solutions.  My question is
are there any instances where we would want to keep the complex solutions and not transform them into real solutions?    I'm looking for a response such as:  we would want to keep the complex solutions in this real-life situation because they would tell us.....

If you don't know the answer, can you send the question to someone that might?  Thanks!