Hey;
I'd appreciate some help with this question;
(from the previous subsection b is an imaginary root of the equation z^5-1=0 and b^4+b^3+b^2+b+1=0)
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Q 13, PART B, MATH HL NOV 08
c) If u=b+b^4 and v= b^2+b^3, show that
i) u+v=uv=-1
ii) u-v= sqrt(5) , given that u-v>0
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for i) Proving that u+v=-1 is not difficult... but i have no idea how to prove that uv=-1, or for ii) how u-v is sqrt(5).
Help would be greatly appreciated