Oops complex

Algebra Level 4

Given \(a\) is a complex number such that \(|a| = 1 \), and \(az^2 + z + 1 = 0 \) has 1 purely imaginary root.

If the real part of \(a\) can be expressed as \( \frac {\sqrt x - y}k \) for smallest positive integer \(x,y,k\), submit \( (x+y)^k \) as your answer.

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