দেওয়া আছে, $$ \begin{aligned} \frac{1-ix}{1+ix}&=a-ib \end{aligned} $$ উভয় পক্ষে মডুলাস নিয়ে পাই, $$ \begin{aligned} \left|\frac{1-ix}{1+ix}\right|&=|a-ib| \\ \Rightarrow \frac{|1-ix|}{|1+ix|}&=|a-ib| \\ \Rightarrow \frac{\sqrt{1^2+(-x)^2}}{\sqrt{1^2+x^2}}&=\sqrt{a^2+(-b)^2} \\ \Rightarrow \frac{\sqrt{1+x^2}}{\sqrt{1+x^2}}&=\sqrt{a^2+b^2} \\ \Rightarrow 1&=\sqrt{a^2+b^2} \\ \Rightarrow a^2+b^2&=1 \end{aligned} $$ সঠিক উত্তর: $a^2+b^2=1$