Question

Q. 60 z is a complex number such that z+1/z=2cos3°,then the value of z^2000+1/z^2000+1 is equal to

Answer 1

So -1+1=0

Hence,A is the right answer

Answer 2

z²⁰⁰⁰+1/z²⁰⁰⁰+1 = 0  if z+1/z=2cos3°

Step-by-step explanation:

Let say z = e^iθ   = Cosθ  + isinθ

1/z = e^-iθ   = Cosθ  - isinθ

adding both

z + 1/z  = 2Cosθ

Comparing with

z+1/z=2cos3°

=> θ = 3°

z = e^3i

z²⁰⁰⁰ = Cos6000° + iSin6000°

1/z²⁰⁰⁰ = Cos6000° -  iSin6000°

z²⁰⁰⁰+1/z²⁰⁰⁰+1

= Cos6000° + iSin6000° +  Cos6000° -  iSin6000° + 1

= 2 Cos6000°  + 1

= 2Cos(5760° + 240°) + 1

= 2Cos(16 * 360 + 240°) + 1

= 2Cos(240°) + 1

= 2(-0.5) + 1

= - 1 + 1

= 0

z²⁰⁰⁰+1/z²⁰⁰⁰+1 = 0

Learn more:

Write z=i in trigonometric form - Brainly.in

https://brainly.in/question/9130337