Imaginary numbers and real numbers?

  • #1
Ilikebugs
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z is either a real, imaginary or complex number, and z^12=1 and z^20 also equals 1. What are all possible values of z?

I know 1 and -1 are them, and I think its also i and -i?
 
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  • #2
We have:



We know so we may divide through by to get:





Now, we observe that satisfies neither original equation, so we are left with:



Next, factor as the difference of squares:



Since , we may write:



Factor again:



Thus, , as you thought. :D
 

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