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If z is a complex number satisfying |z|^...

If z is a complex number satisfying `|z|^(2)-|z|-2 lt 0`, then the value of `|z^(2)+zsintheta|`, for all values of `theta`, is

A

equal to 4

B

equal to 6

C

more than 6

D

less than 6

Text Solution

Verified by Experts

The correct Answer is:
D
We have,
`|z|^(2)-|z|-2 lt 0`
`rArr (|z|-2) lt 0 rArr |z| lt 2`
Now, `|z^(2)+zsin theta | le |z|^(2)|+|z|+|sintheta| le (|z|)^(2)+|z| le 2^(2)+2=6`.
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