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Let S = S(1) nnS(2)nnS(3), where S(1)={z...

Let `S = S_(1) nnS_(2)nnS_(3)`, where `S_(1)={z "in" C":"|z| lt 4}`,
`S_(2)={z " in" C":" Im[(z-1+sqrt(3)i)/(1-sqrt(3i))] gt 0 } and S_(3) = { z "in" C : Re z gt 0}`
`underset(z in S)(min)|1-3i-z|=`

A

`(2-sqrt(3))/(2)`

B

`(2+sqrt(3))/(2)`

C

`(3-sqrt(3))/(2)`

D

`(3+sqrt(3))/(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
Distance of `(1,-3)` form `y + sqrt(3)x= 0`
`|(sqrt(3)xx1-3)/(2)| = (3-sqrt(3))/(2)`
`rArr underset(z in s)min |1-3i-z|=(3-sqrt(3))/(2)`
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