Suppose z1 , z2 , z3 are vertices of an equilateral triangle in an argand plane inscribed in the circle |. z |. = 2 . If z1=1-i√3, z2=a+ib, z3=c+id, where a , b , c , d ∈ R and a c , then |.3a+d-c|. equals to [Note: i = √- 1 ]

Question

Suppose z1 , z2 , z3 are vertices of an equilateral triangle in an argand plane inscribed in the circle |. z |. = 2 . If z1=1-i√3, z2=a+ib, z3=c+id, where a , b , c , d ∈ R and a > c , then |.3a+d-c|. equals to [Note: i = √- 1 ] (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/m-hdj9vtfmm1xpg8fu.jpg" /> ∴ z2=1+i√3 z3 = - 2 a = 1 , b = √3 c = - 2 , d = 0

Q. Suppose $z_{1}, z_{2}, z_{3}$ are vertices of an equilateral triangle in an argand plane inscribed in the circle $∣ z ∣ = 2.$ If $z_{1} = 1 - i 3, z_{2} = a + ib, z_{3} = c + i d,$ where $a, b, c, d \in R$ and $a > c,$ then $∣ 3 a + d - c ∣$ equals to [Note: $i = - 1$ ]

$∴ z_{2} = 1 + i 3$
$z_{3} = - 2$
$a = 1, b = 3$
$c = - 2, d = 0$

Q. Suppose z1​,z2​,z3​ are vertices of an equilateral triangle in an argand plane inscribed in the circle ∣z∣=2. If z1​=1−i3​,z2​=a+ib,z3​=c+id, where a,b,c,d∈R and a>c, then ∣3a+d−c∣ equals to [Note: i=−1​ ]

∴z2​=1+i3​ z3​=−2 a=1,b=3​ c=−2,d=0

Q. Suppose $z_{1}, z_{2}, z_{3}$ are vertices of an equilateral triangle in an argand plane inscribed in the circle $∣ z ∣ = 2.$ If $z_{1} = 1 - i 3, z_{2} = a + ib, z_{3} = c + i d,$ where $a, b, c, d \in R$ and $a > c,$ then $∣ 3 a + d - c ∣$ equals to [Note: $i = - 1$ ]

$∴ z_{2} = 1 + i 3$
$z_{3} = - 2$
$a = 1, b = 3$
$c = - 2, d = 0$