find center and radius of circle represented by |Z-1| =2 , where z is complex number .

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find center and radius of circle represented by |Z-1| =2 , where z is complex number .

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Step-by-step explanation:Squaring the given relation, we have

(z−α)(

z−α

)=k

2

(z−β)(

z−β

)

or (z−α)(

z

−

α

)=k

2

(z−β)(

z

−

β

)

or z

z

−

α

z−α

z

+α

α

=k

2

(z

z

−

β

z−β

z

+β

β

)

or z

z

(1−k

2

)−(

α

−k

2

β

)z−(α−k

2

β)

z

+α

α

−k

2

β

β

=0

or z

z

−

1−k

2

α

−k

2

β

z−

1−k

2

(α−k

2

β)

z

+

1−k

2

∣α∣

2

−k

2

∣β∣

2

=0

or z

z

−

a

z−a

z

+a

a

−a

a

+

1−k

2

∣α∣

2

−k

2

∣β∣

2

=0

or ∣z−a∣

2

=∣a∣

2

−

1−k

2

∣α∣

2

−k

2

∣

∣

∣

β

2

∣

∣

∣

=r

2

Above represents a circle with center at a=

1−k

2

α−k

2

β

and r

2

= as written above.