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In Q.no. 88, if z be any point in A frow...

In Q.no. 88, if z be any point in `A frown B frown C` and `omega` be any point satisfying `|omega-2-i| lt 3`. Then, `|z|-|omega|+3` lies between

A

`-6` and 3

B

`-3` and 6

C

`-6` and 6

D

`-3` and 9

Text Solution

Verified by Experts

The correct Answer is:
D
Clearly, P represents z and R `(omega)` is any point inside the circle `|omega-2-i|=3`.
Clearly, `0 lt PR lt 6 rArr lt |z|-omega | lt 6`
Now, `||z|-|omega|| le |z-omega|`
`rArr -|z-omega| lt |z|-|omega| lt |z-omega|`
`rArr -6 lt |z|-|omega| lt 6 rArr -3 lt |z|-|omega|+3 lt 9`
Hence, `|z|-|omega|+3` lies between `-3` and 9.
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OBJECTIVE RD SHARMA-COMPLEX NUMBERS -Section I - Solved Mcqs
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