Find all complex solutions of P(z) = z^6 -1 and plot them in the complex plane

Jaxson Mack

Jaxson Mack

Answered question

2022-08-02

Find all complex solutions of P(z) = z^6 -1 and plot them in the complex plane

Answer & Explanation

Porter Mata

Porter Mata

Beginner2022-08-03Added 18 answers

P ( z ) = z 6 1 = ( z 2 ) 3 ( 1 ) 3 = ( z 2 1 ) ( z 4 + z 2 + 1 ) = ( z + 1 ) ( z 1 ) ( z 4 + z 2 + 1 ) z = 1 , 1 z 4 + z 2 + 1 = 0 L e t   z 2 = t t 2 + t + 1 = 0 t = 1 ± 1 4 2 = 1 ± 3 2 z 2 = 1 ± 3 i 2 z = ± 1 ± 3 i 2

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