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Let z in C be such that |z| lt 1 .If om...

Let `z in C` be such that `|z| lt 1 `.If `omega =(5+3z)/(5(1-z)` then

A

4 Im `omega gt 5`

B

5 Im `(omega) lt 1`

C

5Re `(omega) gt 4`

D

5 Re `(omega) gt 1`

Text Solution

Verified by Experts

The correct Answer is:
D
`W = (5 + z)/(5(1 - z)), 5w - 5wz = 5 + z`
`z = (5w - 5)/(5w + 3), z = (w - 1)/(w + 3//5)`
`|z| = |(w - 1)/(w + 3//5)| lt 1, |w - 1| lt |w + (3)/(5)|`
Re (w `gt (1)/(5)`, 5 Re (w) `gt` 1
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