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If omega is any complex number such that...

If `omega` is any complex number such that `z omega=|z|^(2)` and `|z-barz|+|omega+baromega|=4`, then as `omega` varies, then the area bounded by the locus of `z` is

A

`4` sq. units

B

`8` sq. units

C

`16` sq. units

D

`12` sq. units

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` `zomega=|z|^(2)`
`implieszomega=zbarz`
`impliesomega=barz`
`:. |z-barz|+|z+barz|=4`
`:. |x|+|y|=2`
which is a square `:.` Area `=8`sq. units
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