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Let S= \z :|z-1|=1 and ( 2-1)(z+ z)-i(z- z)=2 2 \. Let z1, z2 be such that |z1|= z S|z| and |z2|= z S|z|. Then | 2z1-z2 |2 equals :
(4) 2
z=x+iy: |z-1|=1 (x-1)2+y2=1 (circle)
z+ z=2x, z- z=2iy ( 2-1)x+y= 2 (line)
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Eliminating y: (2- 2)x2-(3- 2)x+1=0 x=1 or x=1+ 1 2
z2=1+i, |z2|2=2 (minimum)
z1= (1+ 1 2 )+ i 2, |z1|2=2+ 2 (maximum)
2z1-z2=( 2+1+i)-(1+i)= 2
| 2z1-z2 |2=2
Answer: (4)
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