Question

find cube root of 8 and show that their sum is zero​

Answer 1

Answer:cube root of 8 is 2

Step-by-step explanation:

Answer 2

Correct question:

Find the cube root of unity and show that thier sum is zero.

Answer :

Cube root of unity are : 1 , ω ,ω².

Sum of roots of unity are : 1 + ω + ω² = 0

Explanation :

Cube Root of Unity:

Cube root of unity has 3 roots,

1. 1,
2. ω,
3. ω².

Here the roots ω and ω² are imaginary roots and one root is a rectangular of the alternative root.

The made of the imaginary roots of the dice root of unity is identical to 1(ω.ω²= ω³ = 1),

and the sum of the dice roots of unity is identical to zero.(1 + ω + ω² = 0).

Proof :

1 + ω + ω2

ω= -1 +i√3 /2

ω² = + 1 +i√3 /2

= 1 + ( -1 + i√3 /2) + ( -1 - i√3 /2)

= 1 + ( -1 -1 + i√3 -i√3 /2)

= 1 + ( -2/2)

= 1 - 1 = 0

hence ,

1+ ω + ω2 = 0

(proved that the sum of cube roots of unity are 0)

(#SPJ2)