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I'm having trouble with this:

Let's say we have a homogeneous system of linear equations (HSLE), where all the coefficients are real numbers. Let $f_1, f_2, \dots , f_m$ be the fundamental system of solutions (FSS) for all the real solutions.

Question: How do you prove that $f_1, f_2, \dots , f_m$ is also the fundamental system of solutions for all the complex solutions.

I know that the solutions of the HSLE should form a vector space whose basis is the (FSS), but in this case the FSS is the basis for only the real solutions vector space. I somehow need to show that this FSS is the basis for both real and complex solutions vector space, but how?

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    More context please. Usually the idea behind such proofs is that you have a set of solutions of size $n$, by examination the dimension of your solutions space should be $n$ and so you just need to prove they are independent to deduce they constitute a basis.2012-04-18
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    This is all there is.2012-04-18
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    Ok, well give us an example equation and we'll show you how it works2012-04-18

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