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Number of imaginary complex numbers sati...

Number of imaginary complex numbers satisfying the equation, `z^2=bar(z)2^(1-|z|)` is

A

`0`

B

`1`

C

`2`

D

`3`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` `z^(2)=barz*2^(1-|z|)`
`:.z^(3)=|z|^(2)2^(1-|z|)`…………`(i)`
`implies |z|=2^(1-|z|)` (by taking modulus both sides)
`implies|z|=1`
`impliesz^(3)=1`
`impliesz=1`, `omega`, `omega^(2)`
But `1` is not imaginary
Hence `z=w` or `w^(2)`
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