Cube root of unity

Explanation

1. Cube root of Unity Presented By: Mahrukh Shehzadi MATH CITY

2. Cube root of unity Definition The cube root of unity can be defined as the numbers which when raised to the power Of 3 gives the result as 1.i.e., cube root of unity is the cube root of 1 i.e.,

3. The Cube Root Of Unity Let a number x be the cube root of unity, i.e.

4. Putting the values in quadratic equation = = =

5. = = = = =

6. Hence; ;

7. Prove that each of the complex cube roots of unity is the square of the other Prove that the product of three cube root of unity is one Prove that sum of each complex cube roots of unity is zero Prove that each complex cube root of unity is reciprocal of the other Properties OF Cube Root Of Unity

8. (a) Prove that each of complex cube root of unity is the square of other The Complex cube root of unity are The Complex cube root of unity are and Proof: = = = = = = = = = = = = = = = = = =

9. = = = = = = = =

10. (b) Prove that the product of three cube root of unity is one Three cube roots of unity are 1, and Proof; 1 = 1 =

11. 1 = 1 = 1 = 1 = 1 1. =1 1.1 = 1

12. (c) Prove that sum of each complex cube root of unity is zero i.e., = = =

13. = = = 0 =

14. (d) Prove that each f the complex cube root of unity is reciprocal of other. Proof ; so, or

15. Example: ( i ) = = = = = 1 =

16. ( ii ) = = = =

17. ( iii ) = = = = 1