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

Question

Suppose z1, z2, z3 are vertices of an equilateral triangle whose circumcentre -3+4 i, then mid z1+z2+ z3 mid is equal to (A) 5 (B) 10 √3 (C) 15 (D) 15 √3

Tardigrade Admin · Accepted Answer

Solution: As triangle is equilateral, circumcentre and centroid of the triangle coincides, therefore, (1/3)(z1+z2+z3) =-3+4 i ⇒ |z1+z2+z3| =3 √(-3)3+42=15

Q. Suppose $z_{1}, z_{2}, z_{3}$ are vertices of an equilateral triangle whose circumcentre $- 3 + 4 i$ , then $∣ z_{1} + z_{2} +$ $z_{3} ∣$ is equal to

5

$103$

15

$153$

Solution: As triangle is equilateral, circumcentre and centroid of the triangle coincides, therefore,
$\frac{1}{3} (z_{1} + z_{2} + z_{3}) = - 3 + 4 i$
$\Rightarrow ∣ z_{1} + z_{2} + z_{3} ∣ = 3 (- 3)^{3} + 4^{2} = 15$

Q. Suppose z1​,z2​,z3​ are vertices of an equilateral triangle whose circumcentre −3+4i, then ∣z1​+z2​+ z3​∣ is equal to

5

103​

15

153​

Solution: As triangle is equilateral, circumcentre and centroid of the triangle coincides, therefore, 31​(z1​+z2​+z3​)=−3+4i ⇒∣z1​+z2​+z3​∣=3(−3)3+42​=15

Q. Suppose $z_{1}, z_{2}, z_{3}$ are vertices of an equilateral triangle whose circumcentre $- 3 + 4 i$ , then $∣ z_{1} + z_{2} +$ $z_{3} ∣$ is equal to

$103$

$153$

Solution: As triangle is equilateral, circumcentre and centroid of the triangle coincides, therefore,
$\frac{1}{3} (z_{1} + z_{2} + z_{3}) = - 3 + 4 i$
$\Rightarrow ∣ z_{1} + z_{2} + z_{3} ∣ = 3 (- 3)^{3} + 4^{2} = 15$