Question

If
`z^2+z+1=0`, find
`z^(49) + z^(50) + z^(51) + z^(52) + z^(53)`

Answer 1

-z⁵¹

Explanation:

z⁴⁹ + z⁵⁰ + z⁵¹ + z⁵² + z⁵³

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

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

-z⁵¹