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|z-1|=Max(|z-2|,|z|)Then Re(z)=? Answer is 1/2.Please explain.

|z-1|=Max(|z-2|,|z|)Then Re(z)=? Answer is 1/2.Please explain.

Grade:12

1 Answers

Vikas TU
14149 Points
6 years ago
Dear Student,
z = x+iy
       z-2 = (x-2) + iy
      │z │= x2 + y2 
       │z-2│= (x-2)2 + y2
       
Max(|z-2|,|z|) = x2 + y2             when Re(z)=1
                      = x2 + y2                    when Re(z)>1
                      = (x-2)2 + y2       when Re(z)
 
|z-1|=Max(|z-2|,|z|)
(x-1)2 + y2 = x2 + y2
x = ½ 
Re(z) = ½ 
 
Cheers!!
Regards,
Vikas (B. Tech. 4th year
Thapar University)

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