Question
Sun September 29, 2013 By:
 

if |x-2|=2|z-1| where "z" is a complex number then show that |z|square = 4/3 times real(z).

Expert Reply
Sun September 29, 2013

|z-2| = 2|z-1|

|(x+iy)-2|2 = 4|x+iy-1|2

|x-2+iy|2 = 4|x-1+iy|2

(x-2)2+y2 = 4[(x-1)2+y2]

x2+4-4x+y2 = 4x2+4-8x+4y2

4x= 3x2+3y2

x2+y2 = 4/3. x

|z|2 = 4/3 Re |z|

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