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AI-তৈরি নমুনা উত্তর

Let $Z = 1 - i\sqrt{x^2 - 1}$
$= \frac{1}{2} \left[ 2 - 2i\sqrt{x^2 - 1} \right]$
$= \frac{1}{2} \left[ (x + 1) - (x - 1) - 2i\sqrt{x + 1}\sqrt{x - 1} \right]$
$= \frac{1}{2} \left[ (\sqrt{x + 1})^2 + (i\sqrt{x - 1})^2 - 2\sqrt{x + 1}(i\sqrt{x - 1}) \right]$
$= \frac{1}{2} \left( \sqrt{x + 1} - i\sqrt{x - 1} \right)^2$

Therefore, the square root of $1 - i\sqrt{x^2 - 1}$ is:
$\pm \frac{1}{\sqrt{2}} \left( \sqrt{x + 1} - i\sqrt{x - 1} \right)$