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If z(1)z(2),z(3) and z(4) taken in ord...

If `z_(1)z_(2),z_(3)` and `z_(4)` taken in order vertices of a rhombus, then proves that `Re((z_(3)-z_(1))/(z_(4)-z_(2))) = 0`

Text Solution

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Since ABCD is rohombus , `AB bot BD`.

`arg((z_(3)-z_(1))/(z_(4) - z_(2))) = pm (pi)/(2)`
Therefore `, (z_(3) - z_(1))/(Z_(4) - z_(2))` is purely imagiary.
`therefore RE((z_(3) - z_(1))/(z_(4) - z_(2)))= 0`
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