Determine the set of solutions for

Hint: Try to find an equation in form of a general Circle.

Seriously i have no idea.. im quite good in complex numbers, but this is somehow hard for me

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- Mar 22nd 2010, 04:23 AMcoobeComplex Numbers - Circles
Determine the set of solutions for

Hint: Try to find an equation in form of a general Circle.

Seriously i have no idea.. im quite good in complex numbers, but this is somehow hard for me - Mar 22nd 2010, 06:56 AMSoroban
Hello, coobe!

Quote:

Determine the set of solutions for: .

Hint: Try to find an equation in form of a general circle.

is the distance of point from point

is the distance of point from point

We are told that: .

. . Hence: .

Square and expand: .

Simplify: .

Complete the square: .

Therefore: .

. . The solution is a circle with center and radius 4.

Note: It is known as the*Circle of Apollonius.*

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