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If one of the vertices of the square circumscribing the circle |z – 1| = 2 is 2 + root3 i . Find the other vertices of square.

If one of the vertices of the square circumscribing the circle |z – 1| = 2 is 2 + root3 i . Find the other
vertices of square.
 

Grade:10

1 Answers

Arun Kumar IIT Delhi
askIITians Faculty 256 Points
8 years ago
Hello Student,
Since centre of circle i.e. (1, 0) is also the mid–point of diagonals of square
=>(z1+z2)/2=z0
=>z2=-sqrt3 i
also
(z3-1)/(z1-1)=e^{+-pi/2}
=>z3,z4=(1-sqrt3)+i,(1+sqrt3)-i

Thanks & Regards
Arun Kumar
Btech, IIT Delhi
Askiitians Faculty

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