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If the complex numbers z_1,z_2 " and " z_3 represent the vertices of an equilateral triangle such that |z_1|=|z_2|=|z_3|," then " z_1+z_2+z_3=0

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Solution :Since `z_1,z_2,z_3` are VERTICES of EQUILATERAL triangle and `|z_1|=|z_2|=|z_3|`
`rArr z_1,z_2,z_3` lie on a CIRCLE with CENTRE at origin
`rArr` Circumentre = CENTROID
`rArr ""0=(z_1+z_2+z_3)/(3)`
`thereforez_1+z_2+z_3=0`


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