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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\[ \begin{array} { l l } A) \, & \quad \quad \quad \quad \quad & B) \, \\ C) \, & & D) \, \\ \end{array} \]
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Once you are confident of Complex Numbers, move on to JEE Geometry of complex numbers.