1. Tardigrade
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  4. 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 ]

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

NTA AbhyasNTA Abhyas 2022

Solution:

Solution $\therefore \, z_{2}=1+i\sqrt{3}$
$z_{3} = - 2$
$a = 1 , \, b = \sqrt{3}$
$c = - 2 , \, d = 0$