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Question

If α is a complex number satisfying the equation α2+α+1=0, then α31 is equal to


A

α

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B

α2

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C

1

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D

i

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Solution

The correct option is A

α


Explanation for the correct option:

Step 1. Find the value of α31:

As we know,

ω3=1 (cube root of unity)

ω3-1=0

(ω-1)(ω2+ω+1)=0

ω=1,(ω2+ω+1)=0

(ω2+ω+1)=0

Step 2. α satisfies the equation α2+α+1=0

Roots are ω,ω2 and ω3=1

α31=ω31=ω(ω3)10=ω=α

Hence, Option ‘A’ is Correct.


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