Find the condition that a real value of $x$ will satisfy the equation $\frac{1 - i x}{1 + i x} = a - i b$

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Solution

$\begin{matrix} \frac{1 - i x}{1 + i x} = a - i b m u l t i p l y b y c o n j u g e \frac{1 - i x}{1 + i x} \times \frac{1 + i x}{1 - i x} = (a - i b) (a + i b) 1 = a^{2} + b^{2} \end{matrix}$

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