Hello
1. square root(z)=5th root z,so i need to give those complex numbers in canonical form whom one of their fifth root and square root is equal.
2.When can ε and ε+1 be root of unity at the same time?
In the first one i think one obvious solution is z=0.I tried using trigonometric form,although i need to give the solutions in canonical form.If z is not 0,then it's lenght have to be 1.
sqrt(z) = sqrt(r)* (cos (α+2kπ/2) + i sin (α+2kπ/2))
5th root(z)=5th root(r)* (cos (α+2lπ/5) + i sin (α+2lπ/5)) these 2 are equal when the lenghts are equal and α+2kπ/2=α+2lπ/5 (+2mπ)
so 5th root(r)=sqrt(r) ==> r=0 or r=1.
As for the arguments...I don't see the way to solve that.
In the second one i don't really have an idea to start.
1. square root(z)=5th root z,so i need to give those complex numbers in canonical form whom one of their fifth root and square root is equal.
2.When can ε and ε+1 be root of unity at the same time?
In the first one i think one obvious solution is z=0.I tried using trigonometric form,although i need to give the solutions in canonical form.If z is not 0,then it's lenght have to be 1.
sqrt(z) = sqrt(r)* (cos (α+2kπ/2) + i sin (α+2kπ/2))
5th root(z)=5th root(r)* (cos (α+2lπ/5) + i sin (α+2lπ/5)) these 2 are equal when the lenghts are equal and α+2kπ/2=α+2lπ/5 (+2mπ)
so 5th root(r)=sqrt(r) ==> r=0 or r=1.
As for the arguments...I don't see the way to solve that.
In the second one i don't really have an idea to start.