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If one of the vertices of the square cir...

If one of the vertices of the square circumscribing the circle `|z - 1| = sqrt2` is `2+ sqrt3 iota`. Find the other vertices of square

Text Solution

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The correct Answer is:
`z_(2) = - sqrt(3) I, z_(3) = (1 - sqrt3) + I and z_(4) = (1 + sqrt3) - 1`
Here centre of circle is (1,0 ) is also the mid-point of diagonals of square

`rArr (z_1 +z_2)/(2)=z_0`
`rArr z_2 = -sqrt(3) I " "[where, z_0 =1 0i ]`
`and (z_3 -1)/(z_1-1)=e^(pm ipi 2 )`
`rArr z_3 = 1+(1+ sqrt(3)i),(1pm sqrt(3))pm i = (1-sqrt(3))+i`
and `z_4 =(1+sqrt(3))-i`
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