Let
a=5-i
IaI="\\sqrt{ {5}^2+({-1})^2}\\\\"
IaI="\\sqrt{26}\\\\"
"\\alpha = tan^{-1}(-5)\\\\\na=|a|e^{i\\alpha}=|a|(cos\\alpha+isin\\alpha)\\\\\na^{\\frac{1}{5}}=|a|^{\\frac{1}{5}}e^{i\\frac{\\alpha}{5}}\\\\\na^{\\frac{1}{5}}=\\sqrt{26}^{\\frac{1}{5}}(cos\\frac{tan^{-1}(\\frac{1}{-5})+2k\u03c0}{5}+isin\\frac{tan^{-1}(\\frac{1}{-5})+2k\u03c0}{5})\\\\\n\nk= 0, 1, 2, 3, 4"
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