First I know that the Newton-Raphson formula gives N(z)=z-(f(z))/(f'(z)). If f(z)=z^+1, then N(z)=(z^2-1)/2z
Then the Question asks me to first define two important functions which I did:
1)T(z)=z-i/z+i where is i is imaginery number, 2)N(z)=z^2-1/2z. Hence, I wrote the following in maple:
Then I was asked to show that T(N(z))=(T(z))^2, so I wrote the following commands:
>T(N(z))-(T(z))^2 (I got zero for their difference, so they are equal)
next, the question said the same wave verify that T(N^2(z))=(T(z))^4, so i wrote:
>T(N^2(z))-(T(z))^4 (but I got 0.3239121662-1.392199407I which is a complex number, not zero but WHY?)
and the rest of the questions are as follow:
1) What will be the general result? <-I don't what does it mean by general result :S
2) T(N^k(z)) will be what power of T(z)? <-Is it power of 2k?I have no ideas.
3) Try T(N^3(z)).<-which I know that T(N^3(z))=T(N^2(N(z))), so does T(N^2(N(z)))=(T(z))^6 then?
It would be appreciated If anyone could help me with this/clear up my confusion with questions. thanks.