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 asked this question earlier and the response was no because the formula gives real solutions.  That wasn't 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 hope you can help answer this question.  Thanks!