Question: If z + $\frac{1}{z}$ + 1 = 0, then z<sup>2003</sup> + $\frac{1}{z^{2003}}$ is equal to-...

Question

If z + $\frac{1}{z}$ + 1 = 0, then z²⁰⁰³ + $\frac{1}{z^{2003}}$ is equal to-

Answer 1

Sol. z = w, w² (roots) ; z²⁰⁰³ =w²⁰⁰³ = w²

z²⁰⁰³ + $\frac{1}{2^{2003}}$ = w² + $\frac{1}{\omega^{2}}$ =w² + w = –1

Question: If z + \(\frac{1}{z}\) + 1 = 0, then z<sup>2003</sup> + \(\frac{1}{z^{2003}}\) is equal to-...