(B) We know that the algebraic identity for the sum of cubes is given by: $a^3+b^3+c^3-3abc = (a+b+c)(a^2+b^2+c^2-ab-bc-ca)$ Also,the product of the f

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(B) We know that the algebraic identity for the sum of cubes is given by: $a^3+b^3+c^3-3abc = (a+b+c)(a^2+b^2+c^2-ab-bc-ca)$ Also,the product of the factors involving cube roots of unity is: $(a+b \omega+c \omega^2)(a+b \omega^2+c \omega) = a^2+b^2+c^2-ab-bc-ca$ Substituting this into the identity,we get: $(a+b+c)(a+b \omega+c \omega^2)(a+b \omega^2+c \omega) = a^3+b^3+c^3-3abc$

Class 11 Mathematics 1 Complex Numbers and Quadratic Equations: Complex Numbers De Moivre's theorem and Roots of unity

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If $1, \omega$ and $\omega^2$ are the cube roots of unity,then $(a+b+c)(a+b \omega+c \omega^2)(a+b \omega^2+c \omega) = $

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A
$a^3+b^3+c^3$
B
$a^3+b^3+c^3-3abc$
C
$(a+b+c)^3-3abc$
D
$a^3+b^3+c^3+3abc$

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1 Complex Numbers and Quadratic Equations: Complex Numbers

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De Moivre's theorem and Roots of unity

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$\omega$ is an imaginary cube root of unity. If $(1 + \omega^2)^m = (1 + \omega^4)^m$,then the least positive integral value of $m$ is

MediumIIT 2004

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If $a = \sqrt{2i}$,then which of the following is correct?

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If $\omega (\neq 1)$ is a cube root of unity and $(1 + \omega)^7 = A + B\omega$,then $A$ and $B$ are equal to:

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The number of complex numbers $p$ such that $|p|=1$ and the imaginary part of $p^{4}$ is $0$ is:

MediumWBJEE 2020

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If $\omega$ is a complex cube root of unity,then $(1 + \omega)(1 + \omega^2)(1 + \omega^4)(1 + \omega^8) \dots$ to $2n$ factors is equal to:

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If $1, \omega$ and $\omega^2$ are the cube roots of unity,then $(a+b+c)(a+b \omega+c \omega^2)(a+b \omega^2+c \omega) = $

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$\omega$ is an imaginary cube root of unity. If $(1 + \omega^2)^m = (1 + \omega^4)^m$,then the least positive integral value of $m$ is

If $a = \sqrt{2i}$,then which of the following is correct?

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