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Let A ,B ,C be three sets of complex num...

Let `A ,B ,C` be three sets of complex number as defined below `A={z : I m zgeq1}` `B={z :|z-2-i|=3` `C="|"z : R e(1-i)z")"+sqrt(2)}` The number of elements in the set `AnnBnnC` is 0 (b) 1 (c) 2 (d) `oo`

A

`(10pi)/pi`

B

`(20 pi)/(3)`

C

`(16pi)/3`

D

`(32 pi)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
B
Since `S=S_1 cap S_2 cap S_3`
Clearly the shaded region represents the area of sector
`therefore " "S=1/2r^2theta=1/2xx4^3xx(5pi)/6=(20pi)/(3)`
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