(B) The condition for the origin $(0)$,$z_{1}$,and $z_{2}$ to form an equilateral triangle is given by the relation: $z_{1}^{2} + z_{2}^{2} = z_{1}z_{

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(B) The condition for the origin $(0)$,$z_{1}$,and $z_{2}$ to form an equilateral triangle is given by the relation: $z_{1}^{2} + z_{2}^{2} = z_{1}z_{2}$ Adding $2z_{1}z_{2}$ to both sides,we get: $(z_{1} + z_{2})^{2} = 3z_{1}z_{2}$ From the given quadratic equation $z^{2} + az + 12 = 0$,we have the sum of roots $z_{1} + z_{2} = -a$ and the product of roots $z_{1}z_{2} = 12$. Substituting these values into the condition: $(-a)^{2} = 3(12)$ $a^{2} = 36$ $|a| = 6$

Class 11 Mathematics 4-1.Complex numbers Geometry of complex numbers

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Let $z_{1}$ and $z_{2}$ be the roots of the equation $z^{2} + az + 12 = 0$. If $z_{1}$,$z_{2}$,and the origin form an equilateral triangle in the complex plane,then the value of $|a|$ is:

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A
$4$
B
$6$
C
$12$
D
$3$

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Let $z_{1}$ and $z_{2}$ be the roots of the equation $z^{2} + az + 12 = 0$. If $z_{1}$,$z_{2}$,and the origin form an equilateral triangle in the complex plane,then the value of $|a|$ is:

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