How do you find fifth roots of #1#?

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Answer 1 · 2018-06-26T21:26:52

#=> z = e^(2/5 k pi i ) #

# k ={0,1,2,3,4} #

We are hence find #z# if #z = root5 1 #

#=> z^5 = 1#

Use how #e^(2kpi i ) =1 , AA k in ZZ #

Hence #z^5 = e^(2kpi i ) #

#=> z = e^(2/5 k pi i ) #

For # k ={0,1,2,3,4} #, As any other #k# will give related solutions

Where # re^(i theta ) = rcostheta+ irsintheta#