Complexity!

Algebra Level 3

Let \( z_{1} \) and \( z_{2}\) be the two complex roots of the equation \( z^{2} +az+ b =0 \), where \(a\) and \(b\) are real numbers. Further, assume that the origin, \( z_{1} \) and \( z_{2}\) form an equilateral triangle. Then:

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