If the complex numbers z(1),z(2),z(3) r...

If the complex numbers `z_(1),z_(2),z_(3)` represents the vertices of an equilaterla triangle such that `|z_(1)|=|z_(2)|=|z_(3)|`, show that `z_(1)+z_(2)+z_(3)=0`

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If z_1, z_2 and z_3 , are the vertices of an equilateral triangle ABC such that |z_1 -i| = |z_2 -i| = |z_3 -i| .then |z_1 +z_2+ z_3| equals:

If z_1,z_2,z_3 represent three vertices of an equilateral triangle in argand plane then show that 1/(z_1-z_2)+1/(z_2-z_3)+1/(z_3-z_1)=0

If A(z_1), B(z_2), C(z_3) are the vertices of an equilateral triangle ABC, then arg((z_2+z_3-2z_1)/(z_3-z_2)) is equal to

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In the complex plane, the vertices of an equlitateral triangle are represented by the complex numbers z_(1),z_(2) and z_(3) prove that, (1)/(z_(1)-z_(2))+(1)/(z_(2)-z_(3))+(1)/(z_(3)-z_(1))=0

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If z_(1),z_(2),z_(3) are complex numbers such that |z_(1)|=|z_(2)|=|Z_(3)|=|(1)/(z_(1))+(1)/(z_(2))+(1)/(z_(3))|=1 , then find |z_(1)+z_(2)+z_(3)| .

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If the vertices of an equilateral triangle be represented by the complex numbers z_(1),z_(2),z_(3) on the Argand diagram, then prove that, z_(1)^(2)+z_(2)^(2)+z_(3)^(2)=z_(1)z_(2)+z_(2)z_(3)+z_(3)z_(1).

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CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-ALGEBRA

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