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# Complex numbers watch

1. The question is :
The complex variable satisfies the following relationship
.
Find the maximum and minimum value of such that the given relationship holds.
I have tried converting to Cartesian form but don't really know how to progress.
2. |z+2| = |4z-4i|
(x+2)^2 +y^2 = 4x^2 + 4(y-1)^2
expand and simplify to get equation of circle: (x- 2/3)^2 + (y- 4/3)^2 = 20/9
equation of line through centre and origin is y = 2x
Solve these two simultaneously to get x,y = 0, or x= 4/3, y = 8/3
Therefore minimum |z| = 0
Maximum |z| = ((4/3)^2 + (8/3)^2)^(1/2)
Make sense?

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Updated: January 6, 2017
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