Prove that cube root of unity is equal to the square of another cube root of unity

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Computers,Music and Myself !

Well,thats pretty simple . The cube roots of unity are 1, , . Excluding 1, perform a square of any of the remaining roots (i.e The complex number roots) If you perform a square of , you get , and vice-versa . Hope this answers your question.
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Well,thats pretty simple . The cube roots of unity are 1, [(-1+(sq.root 3)*i)/2] , [(-1 - (sq.root 3)*i)/2] . Excluding 1, perform a square of any of the remaining roots (i.e The complex number roots) If you perform a square of [(-1 - (sq.root 3)*i)/2] , you get [(-1 + (sq.root 3)*i)/2] , and vice-versa . Hope this answers your question. read less
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Tutor

The three cube roots of unity are as follows: 1, (-1+i*sqrt(3))/2, (-1-i*sqrt(3))/2. Let us square the second root /4 =/4 Cancelling one 2 from numerator and denominator. =(-1-i*sqrt(3))/2. which is the third cube root. Thus the second cube root of unity is the square root of the...
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The three cube roots of unity are as follows: 1, (-1+i*sqrt(3))/2, (-1-i*sqrt(3))/2. Let us square the second root [1 - 2*i*sqrt(3) - 3]/4 =[-2- 2*i*sqrt(3)]/4 Cancelling one 2 from numerator and denominator. =(-1-i*sqrt(3))/2. which is the third cube root. Thus the second cube root of unity is the square root of the third cube root of unity. read less
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Computers,Music and Myself !

Well,thats pretty simple . The cube roots of unity are 1, , . Excluding 1, perform a square of any of the remaining roots (i.e The complex number roots) If you perform a square of , you get , and vice-versa . Hope this answers your question.
read more
Well,thats pretty simple . The cube roots of unity are 1, [(-1+(sq.root 3)*i)/2] , [(-1 - (sq.root 3)*i)/2] . Excluding 1, perform a square of any of the remaining roots (i.e The complex number roots) If you perform a square of [(-1 - (sq.root 3)*i)/2] , you get [(-1 + (sq.root 3)*i)/2] , and vice-versa . Hope this answers your question. read less
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MBA

Cal me I will explain.
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Teaching is my passion!!!!

cube root of unity is (1)^(1/3)=1.....and square of cube root is 1...so equal..
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Home Tutor

Ok your answer is correct both are same
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Home Tutor

(+1)x(+1)X(+1) = +1 hence cube root of 1 is also 1 and obviously the square of another cuberoot of unity is also equals to 1. QED
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I teach maths in such a way that students get the concept in easily and score well in exams.

cube root of unity is 1. so lhs is 1. now cube root of unity is 1 and its square is also 1,so rhs is also 1. lhs=rhs hence proved
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M.Tech with 4 years of experience

whatever u do with unity will always be one.
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