|Jan12-10, 05:45 AM||#1|
Solving a complex equation with roots of unity
1. The problem statement, all variables and given/known data
z is a complex number.
Find all the solutions of
(z+1)^5 = z^5
3. The attempt at a solution
Of course one could expand (z+1)^5, but I remeber our professor solving this with roots of unity. Can anyone help?
|Jan12-10, 06:09 AM||#2|
and then just using the roots of unity to find z= 1/(1-w) , w=exp(i*2k*pi/5), k=1,2,3,4.
|roots of unity|
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