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  • If the complex numbers z1 ,z2 ,z3 represent the vertices of an equilateral triangle and |z1|=|z2|=|z3| , then z1+z2+z3=?

If the complex numbers z1 ,z2 ,z3 represent the vertices of an equilateral triangle and |z1|=|z2|=|z3| , then z1+z2+z3=?

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Solution:   Given ,     left | z_1 ight |=left | z_2 ight |=left | z_3 ight |

     Rightarrow     origin is equidistant from z_1,z_2,z_3

      Rightarrow         Origin is the circumcentre of equilateral triangle with vertices z_1,z_2,z_3

      Rightarrow        fracz_1+z_2+z_33=0Rightarrow z_1+z_2+z_3=0

      

Posted by

Deependra Verma

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