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

Let A,B,C be three sets of complex number as defined below
`A={z:lm (z) ge 1}`
`B={z:|z-2-i|=3}`
`C={z:Re((1-i)z)=sqrt(2)}`
`underset(z in s)min|1-3i-z|` is equal to

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
`underset(Zins)min|1-3i-z|`= perpendicular distance of point (1,-3) from the line `sqrt(3x + y=0 rArr (|sqrt(3)-3|)/(sqrt(3+1)=(3-sqrt(3))/(2)`
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