Consider two complex number z and omega ...

Consider two complex number `z` and `omega` satisfying `|z|= 1` and `|omega-2|+|omega-4|=2`. Then which of the following statements(s) is (are) correct?

`Re (z omega)` can never exceed `4`

If `argz = argomega`,then `|z+2|`is equal to `3`

The minimum value of `|z-omega|` to equal to `2`

The maximum value of `|z-omega|` is equal to `6`

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Verified by Experts

The correct Answer is:

A, B

z lies on a unit circle centred at origin and `omega` lies on the line segment joining `(2,0) & (4,0)`

` therefore |z-omega|_("minimum")=BC=1`
`&|z-omega|_("maximum") = AD=5`
Let `z=e^(itheta)implieszomega ==omega e^(itheta)`
where `omega gt 0`
`impliesRe(zomega)=omegacostheta le 4`
As `argomega = 0 impliesargz = 0`
`impliesz "lines at" B(1,0)`
`therefore |z+2|=|1+2|=3`

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