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If |omega|=1, then the set of points z=o...

If `|omega|=1`, then the set of points `z=omega+1/omega` is contained in or equal to the set of points z satisfying.

A

`"Re"(z) le 2` and `"Im"(z)=0`

B

`"Re"(z) le 1` and `"Im"(z)=0`

C

`"Re"(z) le 2` and `"Im"(z)=0`

D

`Re(z) le 1` and `"Im"(z)=0`

Text Solution

Verified by Experts

The correct Answer is:
C
We have `|omega|=1`
`rArr omega=costheta+isintheta`
`z=omega+1/omega`
`rArr z=(costheta+isintheta)+(costheta-isintheta)`
`z=2costheta`
`rArr |"Re"(z)| le 2` and `"Im"(z)=0`
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