If (z – 1)/(z + 1) is a purely imaginary number (z ≠ –1), then find the value of |z|. contexto.140 3 years ago Now,
![\[Let\text{ }z\text{ }=\text{ }x\text{ }+\text{ }iy\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-0e39a18ce1110f0a9bdaf62596041a58_l3.png "Rendered by QuickLaTeX.com")
![\[\begin{array}{*{35}{l}} \Rightarrow ~{{x}^{2}}~\text{ }-1\text{ }+\text{ }{{y}^{2}}~=\text{ }0 \\ \Rightarrow ~{{x}^{2}}~+\text{ }{{y}^{2}}~=\text{ }1 \\ \Rightarrow ~\surd \left( {{x}^{2}}~+\text{ }{{y}^{2}} \right)~=\text{ }1 \\ Hence,\text{ }\left| z \right|\text{ }=\text{ }1 \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-502cb321d22ef0ca56b23cf4f881e1c4_l3.png "Rendered by QuickLaTeX.com")
