Mathematics - Complex Number Question with Solution | TestHub

MathematicsComplex NumberCube Root of UnityMedium2 minPYQ_2018

MathematicsMediumsingle choice

If $α, β \in C$ are the distinct roots of the equation $x^{2} - x + 1 = 0,$ then $α^{101} + β^{107}$ is equal to

Answer:

Solution:

$x^{2} - x + 1 = 0$

Roots are $- ω, - ω^{2}$ .

$α^{101} + β^{107} = {(- ω)}^{101} + {(- ω^{2})}^{107}$

$= - ω^{2} - ω (∵ ω^{3} = 1)$

$= - (ω^{2} + ω)$

$= 1 (∵ 1 + ω + ω^{2} = 0)$

Stream:JEESubject:MathematicsTopic:Complex NumberSubtopic:Cube Root of Unity

⏱ 2mℹ️ Source: PYQ_2018

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