If z 2 + z + 1 = 0 , where z is a complex number, then the value of ( z + z 1 ) 2 + ( z 2 + z 2 1 ) 2 + ( z 3 + z 3 1 ) 2 + ⋯ + ( z 6 + z 6 1 ) 2

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If z 2 + z + 1 = 0 , where z is a complex number, then the value of ( z + z 1 ​ ) 2 + ( z 2 + z 2 1 ​ ) 2 + ( z 3 + z 3 1 ​ ) 2 + ⋯ + ( z 6 + z 6 1 ​ ) 2

TestHub · Accepted Answer

z 2 + z + 1 = 0 ⇒ z = ω or ω 2 so, z + z 1 ​ = ω + ω 2 = − 1 , z 2 + z 2 1 ​ = ω 2 + ω = − 1 , z 3 + z 3 1 ​ = ω 3 + ω 3 = 2 z 4 + z 4 1 ​ = − 1 , z 5 + z 5 1 ​ = − 1 and z 6 + z 6 1 ​ = 2 ∴ The given sum = 1 + 1 + 4 + 1 + 1 + 4 = 12

Mathematics - Complex Number Question with Solution | TestHub

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