ptan466 ptan466

19-01-2020
Mathematics

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If [tex]z^2+z+1=0[/tex], find [tex]z^{49} + z^{50} + z^{51} + z^{52} + z^{53}[/tex]

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MathPhys MathPhys

19-01-2020

Answer:

-z⁵¹

Step-by-step explanation:

z⁴⁹ + z⁵⁰ + z⁵¹ + z⁵² + z⁵³

z⁴⁹ + z⁵⁰ + z⁵¹ + z⁵¹ + z⁵² + z⁵³ − z⁵¹

z⁴⁹ (1 + z + z²) + z⁵¹ (1 + z + z²) − z⁵¹

-z⁵¹

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