# JEE Roots of Unity

This page will teach you how to master JEE Roots of Unity. We highlight the main concepts, provide a list of examples with solutions, and include problems for you to try. Once you are confident, you can take the quiz to establish your mastery.

## JEE Conceptual Theory

As per JEE syllabus, the main concepts under Roots of unity are cube roots of unity and nth roots of unity.

### Cube roots of unity

$x^3-1=0 \Rightarrow x=1,\omega,\omega^2$

Properties of cube roots of unity: $1+\omega+\omega^2=0$

Representation in argand plane

### nth roots of unity

$x^n-1=0 \Rightarrow x=1,\alpha,\alpha^2,...,\alpha^{n-1}$ where $\alpha=e^{i \frac{2\pi}{n}}$

Properties of nth roots of unity: $1+\alpha+\alpha^2+...+\alpha^{n-1}=0$

Representation in argand plane

## JEE Mains Problems

$\begin{array} { l l } A) \, & \quad \quad \quad \quad \quad & B) \, \\ C) \, & & D) \, \\ \end{array}$

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$\begin{array} { l l } A) \, & \quad \quad \quad \quad \quad & B) \, \\ C) \, & & D) \, \\ \end{array}$

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## JEE Advanced Problems

$\begin{array} { l l } A) \, & \quad \quad \quad \quad \quad & B) \, \\ C) \, & & D) \, \\ \end{array}$

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Once you are confident of Complex Numbers, move on to JEE Geometry of complex numbers.

**Cite as:**JEE Roots of Unity.

*Brilliant.org*. Retrieved from https://brilliant.org/wiki/jee-roots-unity/