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

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

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

  1. 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

    =k

    2

    (z

    z

    β

    z−β

    z

    β

    )

    or z

    z

    (1−k

    2

    )−(

    α

    −k

    2

    β

    )z−(α−k

    2

    β)

    z

    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.

Leave a Comment