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Standard XII

Mathematics

Distance Formula

The points ...

Question

The points $z_{1}, z_{2}, z_{3}, z_{4}$ in the complex plans are the vertices of a parallelogram taken in order if and only if

z_{1} + z_{4} = z_{2} + z_{3}

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z_{1} + z_{3} = z_{2} + z_{4}

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z_{1} + z_{2} = z_{3} + z_{4}

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none of these

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Solution

The correct option is C $z_{1} + z_{3} = z_{2} + z_{4}$
As we know that ,
If they represent vertices of a parallelogram then
midpoint of diagonal coincides.
$\\=>{(z_1+z_3) \over 2}={(z_2+z_4) \over 2} \\=>z_1+z_3=z_2+z_4$

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The points z1,z2,z3,z4 in the complex plans are the vertices of a parallelogram taken in order if and only if

The correct option is C z1+z3=z2+z4As we know that ,If they represent vertices of a parallelogram thenmidpoint of diagonal coincides.

The points $z_{1}, z_{2}, z_{3}, z_{4}$ in the complex plans are the vertices of a parallelogram taken in order if and only if

The correct option is C $z_{1} + z_{3} = z_{2} + z_{4}$
As we know that ,
If they represent vertices of a parallelogram then
midpoint of diagonal coincides.
$\\=>{(z_1+z_3) \over 2}={(z_2+z_4) \over 2} \\=>z_1+z_3=z_2+z_4$