Complex Number

z has property that |z-5i|=1 & z₁ is such that |z₁-5|=1

find z₁ with the property that |z-z₁| is maximum

1 Answers

2305

Shaswata Roy ·2013-02-28 05:09:27

On the Argand Plane,
Z lies on the circle with centre O(0,5) and radius 1
Z₁ lies on the circle with centre O'(5,0) and radius 1

For |z - z₁| to be maximum z should lie at H and z₁ should lie at G.

<QOG = 45Â°.
Therefore point z₁ with both the properties is 5+1/âˆš2 - i/âˆš2

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