### Mathematics Class XI

Unit-I: Sets and Functions
Chapter 1: Sets
Unit-II: Algebra
Chapter 5: Binomial Theorem
Chapter 6: Sequence and Series
Unit-III: Coordinate Geometry
Chapter 1: Straight Lines
Chapter 2: Conic Sections
Unit-IV: Calculus
Unit-V: Mathematical Reasoning
Unit-VI: Statistics and Probability
Chapter 1: Statistics
Chapter 2: Probability

# Properties of the cube roots of unity

Let where

Which have some important facts:

(i) , i.e., the two complex roots of the equation are conjugate of each other.

(ii) , i.e., the square root of any one complex roots is the other complex root.

(iii) If we denote to be one complex root, then the three roots are .

(iv) Since is a root of equation , we obtain , where , , i.e., , .

(v) , i.e, the sum of the three cube roots of unity vanishes.

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