Question #78435
Find the sum of the 5th roots of unity.
Expert's answer
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#340153 on Dec 2023
#340153 on Dec 2023
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Formula exp(2*Pi*i)=1 follows from the Euleur's formula exp(ix)=cos(x)+isin(x), where i*i=-1, cos(2*Pi)=1, sin(2*Pi)=0. To find the sum of the 5th roots of unity, the formula for the sum of geometric sequence was applied, where r=exp(2*Pi*i/n) is the ratio and the sum starts from m=0 to m=n-1=5-1=4.
Kindly show all the steps so that it will be easy for us.....