1.

If z_(1), z_(2), z_(3), z_(4) are complex numbers in an Argand plane satisfying z_(1)+z_(3)=z_(2)+z_(4). A compex number 'z' lies on the line joining z_(1) and z_(4) such that Arg((z-z_(2))/(z_(1)-z_(2)))=Arg((z_(3)-z_(2))/(z-z_(2))). It is given that |z-z_(4)|=5,|z-z_(2)|=|z-z_(3)|=6 then

Answer»

AREA of triangle formed by `Z,z_(1),z_(2)` is `3sqrt(7)` SQ units
area of the triangle formed by `z, z_(3), z_(4)` is `(15sqrt(7))/3` sq. units
area of the quadrilateral formed by the points `z_(1),z_(2),z_(3),z_(4)` taken in orders is `(27sqrt(7))` sq. units
area of the quadrilateral formed by the points `z_(1),z_(2),z_(3),z_(4)` taken in order is `(27sqrt(7))/4` sq. units

Solution :`a=B+5`
and `b/6=6/a`
`implies ab=36`
`b^(2)+5b-36=0`
`implies b=4`


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