JEE Main 2022 · 29 Jun · Shift 2 · Mathematics Q1

MathematicsSingle correct+4 / -1Question 1 of 90

Let $\alpha$ be a root of the equation $1+x^2+x^4=0$ . Then the value of $\alpha^{1011}+\alpha^{2022}-\alpha^{3033}$ is equal to :

\alpha

1+\alpha

1+2\alpha

Answer and worked solution

Official answer: A

Roots. $1+x^2+x^4=0$ gives $x^2=\omega$ or $\omega^2$ , and $x^6=1$ . So $\alpha^3=\pm1$ with $\alpha^6=1$ .

Powers. $\alpha^{1011}=\alpha^{3}$ , $\alpha^{2022}=1$ , $\alpha^{3033}=\alpha^3$ : the sum is $\alpha^3+1-\alpha^3=1$ .

(A)

Topics:Roots of unity

JEE Main 2022 · 29 Jun · Shift 2, Mathematics question 1