Simple algebra-calculus question

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1. Homework Statement , and relevant equations

How is A6 arrived at and *how* did they get the "Q" in A6?
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Homework Equations



See above
3. The Attempt at a Solution

Objective: Rid A1 of L. They simply substituted "C" in A2 into A1. But how did they get rid of the L? I don't quite get the algebraic manipulation...please help
 
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What I specifically do not understand is how the exponents, alpha and beta, have been manipulated to be ratios. The only way I think you can do that is by using logarithms, but I do not quite know how.

Anyone have any ideas?
 
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Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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