A) \[0\]
B) \[1\]
C) \[-1\]
D) none of these
Correct Answer: A
Solution :
Let the complex numbers \[{{z}_{1}},\,\,{{z}_{2}},\,\,{{z}_{3}}\] denotes the vertices \[A,\,\,B,\,\,C\] of an equilateral triangle \[ABC\], then if \[O\] be the origin we have \[\overline{OA}={{z}_{1}},\,\,\overline{OB}={{z}_{2}},\,\,\overline{OC}={{z}_{3}}\] \[\therefore \] \[|{{z}_{1}}||{{z}_{2}}||{{z}_{3}}|\] \[\Rightarrow \] \[OA=OB=OC\] \[\therefore \]\[O\]is the circumcentre of \[\Delta \,\,ABC\], hence\[{{z}_{1}}+{{z}_{2}}+{{z}_{3}}=0\]You need to login to perform this action.
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