z = x-iy/x+iy then |z|
You asked:
Given \(z = x - \frac{i y}{x} + i y\) evaluate the expression \(\left\lvert z\right\rvert\).
MathBot Answer:
\[\left\lvert z\right\rvert = \left|{x + y i - \frac{y i}{x}}\right|\]
$$\begin{aligned}\left|{z}\right|&=\left|{x + y i - \frac{y i}{x}}\right|\\&=\left|{x + y i - \frac{i y}{x}}\right|\\&=\left|{y i + x -\frac{i y}{x}}\right|\\&=\left|{y i + x - \frac{i y}{x}}\right|\\&=\left|{x + y i - \frac{y i}{x}}\right|\end{aligned}$$
\(i\) is the imaginary unit, defined as \(i^2 = -1\).