Let A and B be complex numbers such that AB+BA=1 .Then the origin and two points A and B from a triangle which is

AB+BA=1⇒z2−z+1=0 ,where AB=z.So,z=ω or ω2∴AB=-ω or -ω2 so BA=-ω2 or -ω∴|AB|=1⇒|A|=|B|argAB=2π3⇒∠AOB=2π3

Let A and B be complex numbers such that AB+BA=1 .Then the origin and two points A and B from a triangle which is

AB+BA=1⇒z2−z+1=0 ,where AB=z.So,z=ω or ω2∴AB=-ω or -ω2 so BA=-ω2 or -ω∴|AB|=1⇒|A|=|B|argAB=2π3⇒∠AOB=2π3

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Let A and B be complex numbers such that $\frac{A}{B} + \frac{B}{A} = 1$ .Then the origin and two points A and B from a triangle which is

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$\frac{A}{B} + \frac{B}{A} = 1 \Rightarrow z^{2} - z + 1 = 0$ ,where $\frac{A}{B} = z .$

So, $z = ω o r ω^{2}$

$∴ \frac{A}{B} = - ω o r - ω^{2}$

$s o \frac{B}{A} = - ω^{2} o r - ω$

$∴ | \frac{A}{B} | = 1 \Rightarrow | A | = | B |$

$\arg (\frac{A}{B}) = \frac{2 π}{3} \Rightarrow ∠ A O B = \frac{2 π}{3}$

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Let A and B be complex numbers such that AB+BA=1 .Then the origin and two points A and B from a triangle which is

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Let A and B be complex numbers such that $\frac{A}{B} + \frac{B}{A} = 1$ .Then the origin and two points A and B from a triangle which is