Don't Guess

Algebra Level 4

\[\begin{align} A&=\left \{z: \arg (z)=\frac{\pi}3 \right \}\\ B&=\left \{z: \arg \left(z-2-2\sqrt 3i \right)=\frac{2\pi}3 \right \} \end{align}\]

\(A\) and \(B\) are two sets defined as shown above.

Find the number of elements in \(A\cap B\).

Notation: The function \(\arg (z)\) denotes the argument of a complex number.

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