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Question

Let the complex number z1,z2,z3 be the vertices of an equilxeral triangle. let zz0 be the circumcentre of the triangle , then z21+z22+z23−

A
z20
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B
z20
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C
3z20
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D
3z20
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Solution

The correct option is B 3z20
Circumcentre and centroid of equilateral triangle coincides.

Thus , z0=13(z1+z2+z3)

(3z0)2=(z21+z22+z23+2(z1z2+z2z3+z1z3)

so, the triangle is equilateral ,

then

z1z2+z2z3+z1z3=z21+z22+z23

gz20=3(z21+z22+z23)2

(z21+z22+z23)2=3z20

hence, C is the correct answer.

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