Imaginary roots (2)

Algebra Level 4

\(x = \sqrt[a]{n}\)

\(x\) has \(a\) different solutions: \(x_{1}, x_{2}, x_{3}, ..., x_{a-1}\) and \(x_{a}\)

You are given the following:

\[x_{1} = \sqrt{3}\] \[x_{a} = \frac{3 - i\sqrt{3}}{2}\]

Find \(n\).

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