SOLUTION: how do you solve f(x)= x6 - 1 where x6 is x to the sixth power, I have found -1 and 1 as solutions but there are 4 more

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Question 700225: how do you solve f(x)= x6 - 1
where x6 is x to the sixth power, I have found -1 and 1 as solutions but there are 4 more
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+f%28x%29+=+x%5E6+-+1+
+0+=+x%5E6+-+1+
+x%5E6+=+1+
There are 6 solutions, and you have 2 of them:
+1+
+-1+
The other 4 solutions are the imaginary roots:
+root%28+6%2C1+%29+
-----------------
The argand circle has real numbers plotted horizontally
and imaginary number vertically.
The 6 solutions are spaced equally on this circle
60 degrees apart starting with +1:
+1%2F2+%2B+%28sqrt%283%29%2F2%29%2Ai+
+-1%2F2+%2B+%28sqrt%283%29%2F2%29%2Ai+
+-1+
+-1%2F2+-+%28sqrt%283%29%2F2%29%2Ai+
+-1%2F2+%2B+%28sqrt%283%29%2F2%29%2Ai+
--------------------
These are just 30-60-90 triangles scaled down by 1/2
I'll check one of these:
+%28+-1%2F2+-+%28sqrt%283%29+%2F+2%29+%2Ai%29%5E6+
+%28+1%2F4+%2B+%28sqrt%283%29+%2F+2%29%2Ai++%2B+%283%2F4%29%2Ai%5E2+%29%5E3+
+%28+-1%2F2+%2B++%28sqrt%283%29+%2F+2%29%2Ai+%29%5E3+

+1%2F4+-+%283%2F4%29%2Ai%5E2+
+1%2F4+%2B+3%2F4+=+1+
-----------------
Hope this makes sense