Suppose your characteristic equation for the 2nd order equation has complex roots(adsbygoogle = window.adsbygoogle || []).push({});

r+ and r-

These are conjuagtes of each other so the general solution is:

y = Ae^{r+}+ Be^{r-}

My book chooses the constants A and B as conjugates of each other for the reason that this constructs a real solution (not very hard to see if you plug A = E + iF and B = E-iF into the equation above).

But my question is: How does my book know that this constructs all possible solutions that are real?

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# Homework Help: Complex root for characteristic equation

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