Answer to Question #149873 in Complex Analysis for Dhruv bartwal

Question #149873
Find all the 5th roots of (5-i).
1
Expert's answer
2020-12-16T20:10:08-0500

5i=26eiϕ5-i=\sqrt{26}e^{i\phi} , ϕ=sin1(126)\phi=\sin^{-1}({-\frac{1}{\sqrt{26}}})

if z5=5iz^5=5-i then

z=26110eiϕ5+2kπ5,k=0,1,2,3,4z=26^{\frac{1}{10}}e^{\frac{i\phi}{5}+\frac{2k\pi}{5}} , k=0, 1, 2, 3, 4.



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