Answer: Expand (z+1)^5: 5z^4 + 10z^3 + 10z^2 + 5z^1 + 1

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I simply have to expand (z+1)^5

I think I have the solution I am just unsure about the signs:z^5 5z^4 10z^3 10z^2 5z^1 1 Is it alternate signs + - + - ...
 
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I think you meant (z-1)^5

but your signs sound correct, consider how many times each must be multiplied by (-1), eg the z term must be multiplied by (-1)^4 so is even
 
Ye sorry I did mean (z-1)^5, if it was (z+1)^5 would that be the same expansion exceot the signs be all positive. Thanks
 
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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