Error in 3.3.3 Coordinate System from a Vector

[卡卡西]

Shoud be:

here is the proof process:

$$

\begin{aligned}

|v| &=\left| \left(

1 - \frac{x^2}{1 + z}, -\frac{xy}{1 + z}, -x

\right) \right| \\

&= 1 - 2 \frac{x^2}{1 + z} + \frac{x^4}{(1 + z)^2} + \frac{x^2y^2}{(1 + z)^2} + x^2 \\

&= 1 + \frac{

- 2x^2(1 + z) + x^4 + x^2y^2 + x^2(1 + z)^2

}{(1 + z)^2} \\

&= 1 + \frac{

-2x^2 - 2x^2z + x^4 + x^2y^2 + x^2 + 2x^2z + x^2z^2

}{(1 + z)^2} \\

&= 1 + \frac{

-2x^2 - 2x^2z + x^2(x^2 + y^2 + z^2) + x^2 + 2x^2z

}{(1 + z)^2} \\

&= 1

\end{aligned}

$$