Cafe Manila 1.5 Client 64 Bit Os ⏳
Cafe Manila 1.5 Client 64 Bit Os
Cafe Manila is a very special program written especially for managing cyber cafes. Its. Tray – cyberklock clientSodah
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Sodah (surname)
Sodah mine, a Kivu Mines copper mine
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Hathorne Sodah (ward), an electoral ward in the Isle of Wight
Sodah line, a light-rail line on the Isle of WightQ:
Global change of variables
I was trying to do the following:
$z=\frac{z+1}{z-1} $
I wrote
$f(z)=z^2-2$
$z=\frac{z+1}{z-1}$
$f(z)$= $\frac{z^2+1}{z^2-2}$
I know that the solution is $z=\frac{ -1\pm i}{2}$ but what I don’t understand is the step where they change the variable from $z$ to $f(z)$. Can someone explain what is going on under the hood?
Thank you.
A:
The idea is that you are solving for $f(z)$ in terms of $z$. Given $z$, I will denote the solution as $f(z)$. It could be a polynomial, a rational function, or something else, depending on the circumstances.
So, let’s suppose you have
$$f(z)=a_0+a_1 z+\cdots+a_n z^n$$
to solve for $f(z)$ in terms of $z$. Then you have
$$a_0+a_1 z+\cdots+a_n z^n =\frac{a_0+a_1 (z+1)+\cdots+a_n (z+1)^n}{a_0+(a_1-1) z+\cdots+((n-1)a_{n-1}-a_n) z^n}$$
$$\iff
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