SOLUTION: If 1 and w are two of the five roots of w^(5)=1, then show the following: i.w^(2),w^(3), and w^(4) are the remaining roots of w^(5)=1. ii. 1+w+w^(2)+w^(3)+w^(4)=0. iii. w^(5n)=1 f

Algebra.Com
Question 1118051: If 1 and w are two of the five roots of w^(5)=1, then show the following:
i.w^(2),w^(3), and w^(4) are the remaining roots of w^(5)=1. ii. 1+w+w^(2)+w^(3)+w^(4)=0. iii. w^(5n)=1 for any integer n

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


i)




ii)


iii)


RELATED QUESTIONS

If 1 and w are two of the five roots of w^5=1, then show that 1+w+w^2+w^3+w^4 =... (answered by ikleyn)
If 1 and w are two of the five roots of w^5=1, then show that w^2, w^3 and w^4 are the... (answered by ikleyn)
If 1 and w are 2 of the 5 roots of (w)^5 = 1, then prove the following: a) (w)^2,... (answered by Edwin McCravy,mccravyedwin)
If arg((z-w)/(z-w^2)) =0,then prove that re(z)=-1/2,where (w and w^2 are non real cube... (answered by richard1234)
Express as a single logarithm and, if possible, simplify. 2/3[ln (w2 - 16) - ln(w +... (answered by stanbon,MathLover1)
How do I perform the indicated operations and simplify the following: w-4/w-9 – w+1/w+9... (answered by checkley77)
w-2/w-1=4/w+5 (answered by Cromlix)
How do I find all the values of w satisfying the equation? 6-5/w+2=-4/w-1 (answered by checkley71)
Here is my question: [w/{w^2+8w+16}] + [4/{w^2+12w+32}]. I need to add these two... (answered by jsmallt9)