If z1=z2=z3=1 and z1+z2+z3=0, then the area of the triangle whose vertices are z1, z2, z3 is

If z1=z2=z3=1 and z1+z2+z3=0, then the area of the triangle whose vertices are z1, z2, z3 is

  1. A

    33/4

  2. B

    3/4

  3. C

    1

  4. D

    2

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    Solution:

    z1=z2=z3=1

    Hence, the circumcenter of triangle is origin. Also, centroid (z1 + z2 + z3)/3 = 0, which coincides with the circumcenter. So the triangle is equilateral. Since radius is 1, length of side is a=3. Therefore, the area of the triangle is (3/4)a2=(33/4).

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