Question

If z + $\frac{1}{z}$= 2 cos 3ŗ, then z²⁰⁰⁰ + $\frac{1}{z^{2000}}$+ 1 =

• A. 0
• B. 1
• C. –1
• D. 2

Answer 1

Answer: (A)

0

Answer 2

Sol. z = cos 3ŗ ± i sin 3ŗ

Ž z²⁰⁰⁰ + $\frac{1}{z^{2000}}$+ 1 = 2 cos 6000ŗ + 1

= 2 × –$\frac{1}{2}$+ 1 = 0