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  4. Suppose z1, z2, z3 are vertices of an equilateral triangle whose circumcentre -3+4 i, then mid z1+z2+ z3 mid is equal to

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Q. Suppose $z_1, z_2, z_3$ are vertices of an equilateral triangle whose circumcentre $-3+4 i$, then $\mid z_1+z_2+$ $z_3 \mid$ is equal to

Complex Numbers and Quadratic Equations

Solution:

Solution: As triangle is equilateral, circumcentre and centroid of the triangle coincides, therefore,
$\frac{1}{3}\left(z_1+z_2+z_3\right) =-3+4 i $
$\Rightarrow \left|z_1+z_2+z_3\right| =3 \sqrt{(-3)^3+4^2}=15$