Question

If z + z^–1 = 1, then z¹⁰⁰ + z^–100 is equal to

पर्याय

• – 1

• 1

• – i

• i

Answer 1

– 1

Explanation:

Given z + z^–1 = 1 ⇒ z² – z + 1 = 0

∴ z³ + 1 = (z + 1)(z² – z + 1) = 0

∴ z³ = – 1

Now, z¹⁰⁰ + z^–100 = z⁹⁹. `z + z^(-1)/z^99`

= `(-1) z + z^(-1)/((-1))`

= `- (z + z^(-1))`

= – 1.