Phiiii-dom

Level pending

If \(\phi = \sqrt {n + \sqrt {n + \sqrt {n + ...}}}\), where \(\phi\) represents \(\frac {1 + \sqrt {5}}{2}\), and \(\frac {n + ni}{3n - ni}\) is a complex number which can be solved to equal \(\frac {a + bi}{c}\), where \(i^2\) equals \(-1\) and \(a\), \(b\) and \(c\) are positive integers, find the value of \((a + b + c)^{\frac {c}{a + b}}\)?

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