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JEE Previous Year Question

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

Topic: JEE PYQ

Answer: A. Full step-by-step solution below.

A $1$
B $α$
C $l + α$
D $l + 2 α$

Correct answer: A

Solution

(a) x^{4} + x^{2} + 1 = 0 \Rightarrow (x^{2} + x + 1) (x^{2} - x + 1) = 0 \Rightarrow x = \pm ω, \pm ω^{2} where ω = 1^{1/3} and imaginary. So α^{1011} + α^{2022} - α^{3033} = 1+1-1=1

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