The vertices A,B,C of an isosceles right...

The vertices A,B,C of an isosceles right angled triangle with right angle at C are represented by the complex numbers `z_(1) z_(2) and z_(3)` respectively. Show that `(z_(1)-z_(2))^(2)=2(z_(1)-z_(3))(z_(3)-z_(2))`.

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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 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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